These past modal verbs are all used hypothetically, to talk about things that didn't really happen in the past. Could have + past participle means that something was possible in the past, or you had the ability to do something in the past, but that you didn't do it. Would have + past participle can also be used to show if you want to do something or not (volition), we can also use would have + past participle to talk about something you wanted to do but didn't. This is very similar to the third conditional, but we don't need an 'if clause'.