Serverless computing promises to significantly simplify cloud computing by providing Functions-as-a-Service where invocations of functions, triggered by events, are automatically scheduled for execution on compute nodes. Notably, the serverless computing model does not require the manual provisioning of virtual machines; instead, FaaS enables load-based billing and auto-scaling according to the workload, reducing costs and making scheduling more efficient. While early serverless programming models only supported stateless functions and severely restricted program composition, recently proposed systems offer greater flexibility by adopting ideas from actor and dataflow programming. This paper presents a survey of actor-like programming abstractions for stateful serverless computing, and provides a characterization of their properties and highlights their origin. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.