Perfect numbers, which were extensively studied by the Greeks, especially Euclid, have a fascinating history and have engaged the attention of mathematicians for a long time. Euclid devised a method for obtaining even perfect numbers that are closely related to Mersenne’s prime. Based on the updated list of the known perfect numbers, curious properties and endings of perfect numbers with amazing historical backgrounds are discussed. Multiply perfect numbers and sociable numbers, along with interesting observations to stimulate interest for further explorations, are also covered in this chapter.