They have momentum, but not mass (ignore the other explanation, like yes, E=sqrt(m0^2 c^4 + (pc)^2), but so what? m0=0 for photons)

As you can see, momentum, p, is p=E/c, and we know that the energy for light is proportional to its frequency, f, E=hf (h is Plank's constant). So, p=hf/c. When light is absorbed by a material momentum (and energy) conservation apply and it imparts p onto the object. If light is reflected it imparts 2*p, showing this is left as an exercize to the reader