Does a Capacitor Allow DC or AC to Pass? Clarification on Capacitor Behavior

I have read some pages and I have seen that some say that capacitor allow DC and block AC and some say blocks DC and allows AC. Which one is right which is really series problem to me. Pull me out of this. Thank you in advance

An ideal capacitor blocks DC and passes AC.

A capacitor in series will block DC and pass AC. A capacitor will block all DC if you don't account for estimated parallel resistance, which should be enormous, making it typically okay for you to just ignore it. Capacitors will pass AC but pose a certain resistance to it, called its capacitive reactance. On top of that, you have the estimated series resistance, which is typically very small and will resist both DC and AC by the same amount. Capacitive reactance decreases when an AC signal.....well....becomes more AC. The more the current alternates (the higher the frequency), the less the capacitor will resist it.

A capacitor in parallel will shunt AC past the component(s) that it is in parallel with. You could say that it blocks AC in that manner, but that claim would be a tad far-fetched. It _pulls_ the AC away from the other component(s). Again, the amount of AC pulled away will depend on the capacitive reactance of the capacitor.