Mass in Motion
When a particle is accelerated to some velocity, the momentum of that particle is defined using the formula, P = MV, where P is momentum, M is mass and V is velocity. From the equation, a photon can be said to have a mass as long as it is in motion. Since a photon is always in motion, it cannot be said to have a rest mass, or mass at zero velocity. The conclusion by most modern scientists is thus that a photon has no rest mass.
Bending Star Light
Astrophysicists have observed the behavior of light as it passes near a star with a strong gravitational field. If so, some question why this happens if light does not have any mass. One explanation has tried to explain this phenomenon by stating that stars distort the space surrounding them, thereby, affecting the behavior of light in this curved space. This phenomenon is called the space-time continuum.
Zero Rest Mass
Since it is practically impossible to set up an experiment to establish the zero rest mass of a photon, experiments on the limit of the photon rest mass have been obtained that show that the photon rest mass is very close to zero. More improved experiments continue to push this limit even lower, thereby, supporting the concept that a photon indeed has a zero rest mass.
Radiation Pressure
When a photon strikes a surface, it is reflected or absorbed, hence the notion of radiation pressure. This pressure exerted on a surface is the momentum of the photon particle. Since energy and momentum are related, any energy radiated usually falls anywhere between the minimum theoretical value and the maximum theoretical value of the photons. Thus, radiation pressure does not prove that a photon has mass, rather that it is transferable energy.