We give a quick survey of the various fixed point theorems in computability theory, partial combinatory algebra, and the theory of numberings, as well as generalizations based on those. We also point out several open problems connected to these.

翻译：我们快速综述了可计算性理论、部分组合代数与编号理论中的各种不动点定理及其基于这些理论的推广形式，并指出与之相关的若干未解问题。