Yes, "could have" is to express the ability to have done it in the past. "I could have done my homework if I wanted to" "I could have caught that ball" (when someone else failed to) "You should have called if you were running late" "I would've called if I knew you'd worry" PS. there's a contraction Could've (could have) don't confuse it with could of. There is no such phrase "could of", lots of native english speakers get this wrong (they sound alike).

could have done . means you didn't do the job for a certain reason, although you can do it at that time. There is a song: i could have done more. in album : schindler's list

It is used specially with "if clauses" and normal sentences of course : If ----could , I would ( in this case it means if i am able to do i will ,but i am not sure ,but still there is a possibility to do ,it is not excluded !) as CJ said it is a possible action to take in the future ,while you remain unsure if you can or not when you say that ~! While to say : If ----- could have , would have -- ( In this case , the situation terminated and I didnt do cause i couldnt ,so i say if i was able i would have , but when I am saying that ,the possibiltiy of doing is excluded ! As for could used as a past of "can" , that is not the case . I can go tonite ,,,,, you cant say "" " i could go tonite " and it will mean the past , it will mean it is possible for me to go but i am not sure ,if i will be able to do it ! The past of can in this case , will be possibly:"was able" I " was able" to go tonite .

Ciao. Ho mandato un messagio sul chat, but I don't know if you got it. Could (do): This is used for things in the future. Essempio: I wish I could go to the movies tomorrow, but I have to work. or-- If I could get a good grade on the next exam, then that would be great. Could have (done): This is used for things in the past. Essempio: I wish I could have gone to the party yesterday, but I was sick. Spero che questo aiutarti. Ciao.