What were the changes on submarines in 1945-1960?

Before the advent of nuclear power capability and changes in hull design to accommodate the increased speed potential, few changes in WWII era submarines were made. Weapons systems were upgraded, and some boats were converted for Radar Picket service during the Korean War. But essentially they were the same boats - surface ships with limited submergence capability.

Nuclear Power changed everything - with the massive increase in power generating capacity (a single submarine reactor can power a city), and proof of concept of the engineering designs with the Nautilus, submarines were able to go faster, dive deeper, carry more crew, perform more complex missions, carry more weapons, and cruise submerged without having to surface or snorkel to recharge batteries for submerged propulsion. The only limitation on a nuclear submarine is her crew (food, supplies, etc.).

Since then, boats have gotten bigger, weapons and systems more sophisticated, reactors more powerful and efficient, but the overall basic design and engineering stems from the Nautilus. The only significant change from the Nautilus design was her hull, as it was designed along the lines of WWII Fleet boats. The teardrop and cigar hull shapes were found to give greater speed capability during design testing, and were incorporated into all following submarines.