Function-as-a-Service (FaaS) is a cloud service model enabling developers to offload event-driven executable snippets of code. The execution and management of such functions becomes a FaaS provider’s responsibility, therein included their on-demand provisioning and automatic scaling. Key enablers for this cloud service model are FaaS platforms, e.g., AWS Lambda, Microsoft Azure Functions, or OpenFaaS. At the same time, the choice of the most appropriate FaaS platform for deploying and running a serverless application is not trivial, as various organizational and technical aspects have to be taken into account. In this work, we present (i) a FaaS platform classification framework derived using a multivocal review and (ii) a technology review of the ten most prominent FaaS platforms, based on the proposed classification framework. We also present a FaaS platform selection support system, called FaaStener, which can help researchers and practitioners to choose the FaaS platform most suited for their requirements.