Cosmos hurts my brain

Ok so can anyone point me in the right direction maybe? I'm a real amateur with science and physics but I have a question

Is the speed of light constant and finite? If so, then when what happens when light fails to exit a black hole? If the light cannot escape the pull of gravity doesn't that mean that the light waves need to be eventually slowed down and then stopped? Or does the trajectory of the light get warped and it circles it like a drain before spinning infinitely around the centre of the event horizon? Go easy on me I didn't do science past year 10 :/