We know that the photon itself is massless particle $m_0=0$. But we also know, that the mass of the objects does increase with their energy. And we know that under certain circumstances (gravity, collision with objects) the light does behave like a beam of particles that do have a mass.
Now, this is the equation to get the (relativistic) mass of the object with certain speed: $$m=\frac{m_0}{\sqrt{1-v^2/c^2}}$$ We already do know some things: $m_0 = 0$, $v = c$. $$m=\frac{0}{\sqrt{1-c^2/c^2}}$$ $$m=\frac{0}{0}$$
Expression $\frac{0}{0}$ is not equal to 0. So what is this?
I'll remind you of those weird clock that are run by light - I failed to find any images, but the clock principle was similar to windmill. And it works.
Also there was an idea to make long-distance autonomic spaceships that are pushed by light rays from stars.