An oxygenator (10) combines, in a single structure, a heat exchanger (32), a gas exchanger (34) and an arterial filter (38). Such an oxygenator permits fewer fluid connections and thus may simplify an extracorporeal blood circuit, including a heart-lung machine and a blood reservoir, in which it is used. In some cases, the oxygenator (10) may be configured to include multiple purge ports (28, 30) for purging bubbles both before and after filtering the blood.