Could we curve the flight path of a photon? I was wondering about photon's interaction with matter, and why photons dont slow down. They seem to always bounce in a straight line at the same speed (I think), as if some force is charging them forward after the bounce. First, what is this? I've heard of experiments where we actually did slow them down, and they can be absorbed and bounced by matter, so I wanted to know if they interact with matter in such a way that we could spin one, like a curve ball thrown by a pitcher, and make them curve their flight path. 
Can someone explain this, in English (back it up by math if you need to but I'm not a physicist, I just like to learn about the fundamental ideas)?
 A: The lenses in my reading glasses bend the path of photons, as does gravity. In matter photons move at slower speed than $c$. In Bose-Einstein condensates they can even be brought to a halt. 
A: Adding to Anna's response,
In small scales, photons wont slow down because they are thought of as being relativisitc quantum fields in all their possible interaction channels. However, at large scales (cosmological distances) there is an indication of slowness (delay in arrival time)-- either due to a varying gravitational potential (due to non-flat spacetime fabric as mentioned by Anna) or due to the expansion of Universe itself.
Einstein himself argued that in the absence of gravity and expansion of Universe (which he was reluctant to believe in the latter) light would never slow down or speed up and was able to show it explicitly.But, current frontier research at small-scale, everyday life and large scale are positive after all that they are seeing a varying speed of light. (Related sources: Varying Speed of Light)
A: 
so I wanted to know if they interact with matter in such a way that we could spin one, like a curve ball thrown by a pitcher, and make them curve their flight path. 

Photons interact with matter with the electromagnetic interaction. There can be elastic scattering of a photon of energy E with a charged particle and only the angle will change , but it happens at one point in space and time , not a continuous curve.
So individual photons do not act like a classical ball, which should be expected as they are quantum mechanical entities.
Light , which is composed out of an innumerable number of photons  does display a "curve" in space collectively in a lattice, by additions of the behavior of the collective photon ensemble, as in optical fibers.
There also exists gravitational lensing of light :

A gravitational lens refers to a distribution of matter (such as a cluster of galaxies) between a distant source and an observer, that is capable of bending the light from the source, as it travels towards the observer.

Individual photons are elastically scattering but the light wave displays curvature.
