If you think of “the electromagnetic field” as being [literally] everywhere, then any localized vibration in that field is “a photon” (regardless of whether that vibration is exhibiting the properties of a particle or a wave).
That localized (but never perfectly localized) vibration, or photon, is the carrier particle of electromagnetic energy (one of four forces).
Wave-Packets, Frequencies, Wave Forms, and Other Properties of Light
Light follows a few other rules that relate to its particle and wave-like nature too.
Photons always vibrate at any frequency greater than zero (if part of the electromagnetic field isn’t vibrating, then isn’t a photon).
Photons typically exists as a packet of waves that create an aggregate wavelength (rather than existing as a single wave). From this perspective, we can consider a photon “a packet of waves” that can emit or absorb other electromagnetic waves (“photons”).
When the photon travels, it travels as a transverse wave of probable locations of vibrations in the electromagnetic field in a single direction unless obstructed. A photon can “quantize” (jump to) to any probable location in that field (a range of possible next locations based on light speed and Planck units, AKA the physical constants).
Any part of the charged field, whether it is acting like a wave or a particle, and whether its location is actual or probable, and whether its a single low energy wave or a high energy wave packet, is “a photon”.
When photons vibrate at a certain range of frequencies (wavelengths of about 390 to 700 nm), based on their energy content, we call the corresponding wave packet of electromagnetic radiation “visible light” (a small range of frequencies in the electromagnetic spectrum).
When we consider all possible wavelengths (which correspond to the frequency at which a photon vibrates, which corresponds to its energy content) we call this the electromagnetic spectrum (a spectrum of possible wavelengths of electromagnetic energy, which can be described as localized vibrations in the electromagnetic field traveling in a wave-like manner, of which measurable excited states are called particles). 
Whatever my above explanation lacks, the videos and additional facts below should be able to clarify. First up, I suggest the following PBS Space Time video which has an excellent explanation of wave-particle duality. I also strongly suggest at watching the equally informative Fermilab video below.
TIP: So if light is just electromagnetic waves, “what are electromagnetic waves made out of?” As the video above says, “we don’t know exactly”. A photon has properties that relate to motion (spin, light speed, energy content, quantizes to orders related to the planck length). A photon has momentum, but not mass. Photons can add to the potential energy of a system. Photons are responsible for “charge” (think electricity). We can say things about photons, but there is no real underlying widget to discuss.
TIP: Although the photon’s wave and particle qualities are complementarity (they can’t be observed or measured at all at the same time), they have been shown through experiment to be two observable aspects of a single phenomenon.
TIP: With the above in mind, the classical concepts of “particle” and “wave” don’t fully describe the behavior of quantum-scale objects. In this same way, the quantum field nature of light is only one model for describing electromagnetic energy, it can also be described as a localized set of points in space and time. Despite working theories, there is no fully agreed on way to describe particle-wave duality.
TIP: All elementary particles have particle-wave duality, and all can be understood as quantum fields that permeate all of space. This concept is called Quantum Field Theory (QFT), and the specific rules for light (and most quantum particles that make up matter) are encapsulated by Quantum Electrodynamics (QED). On a deeper level, single wave-particles can be thought of as strings as well (1 dimensional points that describe single waves). Super String Theory (which describes all quantum particles as strings), QFT, and QED are “models” (AKA theories) for understanding quantum behavior (not the only way to understand quantum behavior). 
Quantum Field Theory by Fermilab. The Fermi National Accelerator Laboratory does some really excellent videos, this is a very simple explanation of quantum field theory (which explains the particle-wave-field nature of energy). The videos we curated for this page tend to be mind-blowing, so even if you stop reading, consider watching the videos below (especially the Richard Feynman one).
FACT: Sir Isaac Newton called the single smallest particle of light “a corpuscle” in his book Opticks.
Sometimes photon fields are described a singular “the electromagnetic field” and sometimes as multiple “fields” (a field per photon or chunk of photons). There is no proper way to think of this, a single field is probably simpler, but multiple fields work too. You can read the long answer as to why here.
The gravitational field and the electromagnetic field are the only two fundamental fields in nature that have an infinite range and a corresponding classical low-energy limit, which greatly diminishes and hides their “particle-like” excitations. The photon was the only particle that we found the field of before the particle itself, and we notably haven’t even proved “the graviton” (the gravity particle) exists yet.
At its lowest energy state (which can be described as approaching zero), a single photon can be measured as a single particle and a corresponding single (very long) wavelength (the lowest measurable charged state in a photon field). This single photon still has the same wave-like and particle-like properties as higher energy photons.
The longer the wavelength, the harder it is to measure a photon in a single place in space, the shorter the wavelength the easier.
The longer the wavelength the “colder” the light is, the shorter (the higher frequency) the “hotter”.
All photons exist as a transverse wave, i.e.a wave vibrating at right angles to the direction of its propagation, in quantum superposition, i.e. existing in multiple states at once). Despite its wave-like existence, we can still consider the photon a particle.
We can’t localize a photon perfectly in space as it has no mass (and only momentum). Despite this we CAN measure a photon over space and time, measure excited states in space to a high degree of accuracy, and can generally use experiments to confirm light’s wave-like and particle-like nature (for instance via the famed double slit experiment).
All energy, from particles, to sound, to gravity travel as either classical (consistent) or quantum (quantized) waves. “Wave” describes how the energy travels through a field, particle describes a measurable state in a charged field. All waves transfer energy. Learn more about the types of waves.
Like classical and quantum waves, classical fields are consistent fields and quantum fields are fields in which quantization occurs.
TIP: The famed slit experiment is a simple version of the dual-slit experiment which shows off particle-wave duality and the “observer effect” (where measuring affects particle behavior). The observer effect is a separate, but related, phenomena.
FACT: All the above statements are essentially true, and reasons like this are is why mathematician and author Lewis Carroll parodied quantum physics (and related mathematics) in his classic “Alice’s Adventures in Wonderland” (Authors note: still gotta prove this Lewis Carroll factoid, heard it once and it blew my mind, still haven’t been able to confirm it). 
The Original Double Slit Experiment. The double slit and observer effect is so strange that it should either be ignored or studied in detail. Generally it seems to suggest photons can be entangled in time and space. See here.
Is Light Both a Particle and a Wave? – Technical Answer
The photon is a charge in the electromagnetic field, propagated in a unidirectional transverse wave in a state of quantum superposition, that exhibits quantized measurable excited energy states we call particles. The photon travels in a single direction forever at light speed unless impeded. A photon can emit other photons and can absorb other photons, within limits. Although a photon “particle-wave-field” can change energy content and radiate away other photons, it is always massless. Yet, all composite particles with mass have “absorbed photons”, and photons can add to the mass of a system. Visible light is a specific frequency of electromagnetic radiation in the electromagnetic spectrum which arises from electromagnetic field fluctuations (frequency changes in the electromagnetic field). 
TIP: When talking about photons we can call the electromagnetic field “the photon field”. In Quantum Field Theory we can consider each type of particle to have its own field.
TIP: When talking about electromagnetic radiation there is a “far field” in which radiation can travel forever, and a local oscillating “near field” where energy travels back and forth. These fields exists within the large electromagnetic field that permeates all of space.
What Happens When a Particle Stops Moving in a Single Direction?
When a Particle, like a photon, is impeded it typically changes direction (either angular or linear momentum), emits some of its energy content as radiation (essentially creating new photons), and can even bind with other particles adding to their mass, or changing their spin or charge. See mass-energy equivalence and rest-mass versus relativistic mass.
TIP: Particles can never touch without a nuclear reaction occurring, but fields overlap constantly. A photon may be massless, but (as you know from any reflective surface), a photon particle can bounce off mass and change direction (like with the Higgs Boson). Interestingly there is no way to determine which photons will be reflected, it is simply a matter of probability, despite this all we can predict the total amount of reflection that will occur with consistent accuracy. 
Should Quantum Fields be Measured as Fields, Particles, or Waves?
Whether we treat quantum fields as waves or particles just depends on what we are measuring or doing. If I want to measure the angular momentum of a photon, i’ll be looking a particles, if I want to build a laser, i’ll use particles, if I want to light a room or understand refraction, i’ll look at waves, if I want to explore the quantization of energy, i’ll likely just focus on fields.
A Rough Analogy of Electromagnetic Energy as Water Flowing Down a River
To end this page, let’s consider an analogy.
If you think of electromagnetic energy as a flowing river then you’ll have a rough analogy for a visual of the quantum nature of light. We can consider the river to be “water” or we can consider it as “droplets”. It moves forward in one direction at a constant speed unless impeded, it waves and ripples, and when it interacts with something it splits into droplets, and then the droplets come back together as water.
We know the droplets are mostly bound to or near the path of the water (its field), while there is a slight probability a splash can occur outside the path of the river, but only within a certain distance. Water can act as both droplets and a wave, it can be used to power things, and soaking up water can add to the weight of an object. Electromagnetic energy very roughly works the same way, but only roughly, after-all, water itself has a core property of electromagnetic energy in its atomic makeup (quarks, electrons, etc, i.e. two hydrogen atoms and one oxygen atom which form the H20 molecule, and are themselves elements made of elementary particles).
Quantum Electrodynamics. This video is the headiest of all, but for those who made it to the end and don’t want the documentary version above, here is the hardcore quantum electrodynamics video for beginners.
TIP: Still curious about the nature of light? See our page on the nature of light. Want to learn more about particle wave duality, see our page on particle-wave duality and quantum fields.
While the building blocks of the universe, including “light”, are best understood as localized vibrations in “energy fields” that travel in a wave-like manner, rather than solid floating spherical billiard balls (i.e. quantum field theory), it is logical to understand the building blocks of the standard model (including light AKA electromagnetic energy AKA the photon) as particles first, and then to consider their field-like, and especially wave-like, nature second.
With the above understood, all this can be simplified to: [just like all other quanta] “light is both a particle and a wave”.
Thomas DeMichele is the content creator behind ObamaCareFacts.com, FactMyth.com, CryptocurrencyFacts.com, and other DogMediaSolutions.com and Massive Dog properties. He also contributes to MakerDAO and other cryptocurrency-based projects. Tom's focus in all...