It's actually both. You process the past (how that is done can vary widely) in order to rework how things in the past affect things in the present.

I had HUGE issues with repression and suppression. What I find CBT helps with is forcing myself to really pay attention to my thinking which is a real problem for those of us who repress memories. My T worked with me on kind of working backwards; it's a bit hard to explain but I'll take a stab at it.

So, hypothetically something is going on in my life that is causing me a problem (anxiety, depression, anger, etc. -- strong emotional reaction generally). I am reacting triggered by something probably in a way that is out of proportion to what is actually going on. T has me stop and work backwards; what was I thinking just before I had that reaction (because I am so good and repression, it is often hard to even figure that out). It can take some digging, but generally I'll find my reaction is one either I would have had earlier in life to something that happened to me or the reaction has become habitual because of old beliefs I have about life or myself that developed due to issues earlier in life. Then we look at those incidents, those beliefs, where did they come from, do they still serve me positively now or can I consider changing those types of thinking, etc. since they may not have a thing to do with my reality now? That isn't surface work; that is deep and emotional and often very painful work. But I find over time that I am able to leave the past in the past and move forward.