What is the name of the effect where light bends around massive objects?

Gravitational lensing, and it was the observation that made Einstein famous overnight. General relativity predicts that mass curves spacetime and light follows that curvature, and Arthur Eddington photographed stars near the Sun during the 1919 eclipse to check whether their apparent positions had shifted. They had, by about the predicted amount.

It has since become a tool rather than a test. A massive galaxy cluster in front of a distant one acts as a lens, magnifying objects that would otherwise be far too faint to see - so telescopes get to use the universe's own optics, and some of the most distant galaxies known were found this way. When the alignment is near-perfect the background object smears into a ring, called an Einstein ring.

It also weighs things that emit no light. The amount of bending gives the mass doing the bending, and when astronomers do that arithmetic for galaxy clusters they find far more mass than the visible matter accounts for - which is one of the strongest lines of evidence for dark matter. In one case, the Bullet Cluster, two clusters have collided and the lensing mass has visibly separated from the hot gas, which is difficult to explain by modifying gravity instead.