First - I'm just a guy (geophysics undergrad - many years ago), so I'm just giving my ideas - not necessarily correct or complete.
I'm struggling with this as well.- along with fields. Here's what I see so far. Feyman says a photon is a particle in QED - forget waves. Sean Carroll says forget particles and focus on fields instead. A particle is just the result of a collapse of the uncertainty of position and momentum. But he's really speaking of probability fields - with the probability defined but QED theory (probability amplitudes based on time oscillations). If we think of each location in space of a photon at a particular time, it has a certain probability to be in another location in space at another time - each of these other locations has a probability of being there depending on the distance. If you think about it, areas of equal distance from the starting point creates a sphere. So the probability fields are infinite numbers of spheres, representing the same distance from the starting point. What seems to matter is time not distance, but since the photon is traveling at constant speed (c), if the medium traveling through is uniform, then location in space means the same amount of time has elapsed. Each of these probability spheres is really what a field is defined as. An aside - recognizing it as fields helps conceptually and mathmatically, but I don't think it necessary helps with the concept that Newton struggled with - action at a distance.
But there's also another wave concept besides wave-particular duality - probability waves - that makes no sense to me if my definition of a wave is correct - interaction with adjacent particles/positions.
Here's what I mean. What's the difference between a wave and a field? I think the answer is that a wave interacts with its neighbors. Like dominoes or water. That's the thing that Sean Carroll and others leave out in layman talks they give. Waves "propagating" through the field. Amber waves of grain move in the same direction from a force (the wind) but they do not push on each other - well maybe a little but it's primarily the wind. Feyman says photons and electrons are not acting as a wave to explain QED. He says it's been tested - I believe him but if so that means that each photon is not interacting with it's neighbor. Predicting whether a photon from one source location will arrive in another location is independent of other photons. Each photon carries an internal mechanism - a probability mechanism that oscillates from zero to a max probability - who knows how this works. It's independent so it can't be a wave. It's a disturbance in space-time field that can be thought of as a particle. And it becomes that particle only when we bother to measure it; otherwise it is just a probable disturbance in a particular location in the space-time field - with the probability changing in spheres of equal probability throughout the universe.
What's the conclusion of my rambling? Modern physics says that waves are out. Even the concept of probability waves is misleading. Unless and until we discover some interaction between particles. But I think physics still think of light "propagating" through space, when QED says it's more about probabilities. I don't think you can think propagating without waves - so the real duality is you use whichever concept works best as an approximation given the problem you're trying to solve, but the best understanding of the universe is not-wavelike, but a weird probability situation. There are instances where you can use probability computation to solve the problem but other times wave works as well and might be easier mathmatically.
To all of you that know more than I do (a huge number) - please remember to use terms like "misled" "lacks complete understanding", etc., as opposed to "moron" "feather brain" etc. Partly I'm writing this to get it clear in my own head - and things are very fuzzy there most of the time.
Lews