The serverless model represents a paradigm shift in the cloud: as opposed to traditional cloud computing service models, serverless customers do not reserve hardware resources. The execution of their code is event-driven (HTTP requests, cron jobs, etc.) and billing is based on actual resource usage. In return, the responsibility of resource allocation and task placement lies on the provider. While serverless in the wild is mainly advertised as a public cloud offering, solutions are actively developed and backed by solid actors in the industry to allow the development of private cloud serverless platforms. The first generation of serverless offers, “Function as a Service” (FaaS), has severe shortcomings that can offset the potential benefits for both customers and providers—in terms of spendings and reliability on the customer side, and in terms of resources multiplexing on the provider side. Circumventing these flaws would allow considerable savings in money and energy for both providers and tenants. This chapter aims at establishing a comprehensive tour of these limitations, and presenting state-of-the-art studies to mitigate weaknesses that are currently holding serverless back from becoming the de facto cloud computing model. The main challenges related to the deployment of such a cloud platform are discussed and some perspectives for future directions in research are given.