Ships were sent out in the days and weeks following the sinking, to recover the bodies. Due to the coldness, and the fact that most people died through freezing to death, not from drowning, and they were wearing life vests, there were large numbers of frozen, dead Titanic victims, well-preserved, floating around the sea lanes for quite some time, bobbing upright in the water. Many ships reported seeing them in large clusters, but by the time the ships came to pick up the bodies, they had dispersed and many were likely unrecovered.
Sometimes, publicity surrounded the recovery, as they found a few famous people's bodies. Then, there was a perfectly preserved body of a young boy who was recovered, from 3rd class. This moved a lot of people, and there ended up being a big search to find out who he was, and many people donated money so that he would have a funeral and be buried in style.