Defining photons I've read every book for my course and all of them describe photons as wave-packets/"bursts" of the EM wave. I just can't appreciate this view of photons. 
From what I've gathered on photons: Photons are uncharged fundamental particles that are the quanta of light (smallest physical entity). Thus photons carry part of the wave, each with E = hf. 
Is this viewpoint correct? In a beam of light, are millions of photons flying in the direction of the beam? 
I feel at unease with my understanding, could someone explain what exactly is a photon and how it works in a light wave?
 A: The wiki article you quote is succinct, the photon is an elementary particle in the table of elementary particles of the standard model of particle physics.
It is a quantum mechanical entity which means it is described by a wavefunction whose square gives the probability of finding the photon at (x,y,z) at time t. The double slit experiment  with a single photon at a time is instructive. It shows
a) the individual photons at first look as if they arrive randomly on the screen
b) slowly an interference pattern is seen in the x,y of the screen, accumulating a probability distribution which is the square of the wave function for this experiment: photons + two slit boundary conditions.
c) that coherent  light is composed of  a great number of  single photons that work in confluence , 
d) that the frequency of the probability distribution is the same as the frequency of the classical electromagnetic wave : the same interference pattern.
This happens because the wavefunction of the individual photons is the solution of a form of the Maxwell's equation with operators acting on the wave function. Thus the quantum mechancical underlayer joins smoothly with the classical solutions. 
For advanced reading of how the classical electromagnetic wave emerges from photons have a look here. It needs graduate courses to really understand.
