Can gravity affects light?

Yes, light is affected by gravity, but not in its speed. General Relativity (our best guess as to how the Universe works) gives two effects of gravity on light. It can bend light (which includes effects such as gravitational lensing), and it can change the energy of light.

How does gravity interact with light?

When photons travel through the region near a massive object that has caused significant warping, they follow curved paths because the space-time through which they are moving is curved. While it is true that photons have no mass, it is also true that we see light bend around sources with high mass due to gravity.