The Gestapo was the secret police of Nazi Germany. It had a hybrid status as part of the state on one hand, and part of the Nazi Party in the other, via the Reichssicherheitshauptamt. It was dissolved in 1945, after Germany had surrendered. High-ranking officials were put on trial, and faced prison or sometimes death. Most mid- to low-level members were fired from public service. Some were rehired in the 1950ies and continued to work as policemen, but the Gestapo as an organisation was not ressurected.
The SS was also dissolved in 1945. The situation for its members was a bit different, as the SS included the Waffen-SS, which included people who had been drafted into the war. Again, high-ranking officials were tried and punished. Others fled, especially to Spain and South America. Many ordinary members joined the french foreign legion. The rest did the same as members of the Wehrmacht did, and tried to find a livelihood in post-war Germany. It is only alive in the way the Neo-Nazi organisations lay a claim to their memory.