After the war the patrol role was generally taken over by conversions of civilian airliners that had range and performance better than most WWII bombers. The latest jet-powered bombers of the 1950s did not have the endurance needed for long, over-water cruising. The main threat to the United States throughout the 1960s and into the 1980s were Soviet submarines, which were found primarily with the use of sonobuoys, and then attacked with homing torpedoes.
Today the threat of a large scale submarine attack is remote, and many forces are downsizing their patrol aircraft fleets. Those still in service are used primarily for counter-smuggling and fishing limits enforcement duties.