"I was told that light has no mass. I also know that gravity is a force between two or more massive objects. So, how is it that massive objects can affect the trajectories of light particles, or photons?"

Excellent question.

It combines two different gravitational models: Newtonian and Einsteinian. (I don't know if that is an actual word, either.) By reconciling these two models, we will hopefully address your question.

We'll attempt to be methodical in our approach.

1. Isaac Newton described gravity as an attractive force mediated between all massive objects.

2. A photon is a massless 'particle," meaning it has no rest mass.

3. Light photons are affected by gravitational fields, which Albert Einstein predicted in his General Theory of Relativity.*

These three statements seem irreconcilable, until we explain that Newton's description isn't entirely accurate. His notion of gravity as a force exerted between two objects was consistent with his observations. However, Einstein described gravity not as a force between particles, but as deformations that massive objects create in their local space-time geometries. To illustrate this principle, we employ the well-worn example of a bowling ball resting on a taut rubber sheet. The ball deforms its local region of space-time, producing an "indentation" around it. Imagine tossing a handful of ball bearings across this sheet. Those ball bearings closest to the ball will move toward it as a consequence of the 'well' it created around it. Those ball hearings farthest away will be only slightly affected (or unaffected) by the bowling ball's 'dent.'

In space-time, any massive object will induce a distortion proportional to its mass and inversely proportional to its size. (A neutron star's gravity well will be much deeper than a regular star's as neutron stars are about twice as massive as the Sun, but are as small as large cities.) These space-time indentations affect the path of light because photons propagate through space-time.

If - and, this is one of those impossible IF's that one tends to find in February pomegranate bushes - gravity were merely a force between massive particles, then light would not be affected by planets, stars or even galaxies. They would move along unperturbed trajectories through space-time. As it is, light can't escape gravity's influence any more than we can.

I hope this answer proves helpful.

 *In 1919, Sir Arthur Eddington led an expedition to observe the star field behind a solar eclipse. His observations verified that massive objects such as the Sun can 'bend light.'