Although historically the term serverless was also used in the context of peer-to-peer systems, it is more frequently associated with the architectural style for developing cloud-native applications. From the developer's perspective, serverless architectures allow reducing management efforts since applications are composed using provider-managed components, e.g., Database-as-a-Service (DBaaS) and Function-as-a-Service (FaaS) offerings. Blockchains are distributed systems designed to enable collaborative scenarios involving multiple untrusted parties. It seems that the decentralized peer-to-peer nature of blockchains makes it interesting to consider them in serverless architectures, since resource allocation and management tasks are not required to be performed by users. Moreover, considering their useful properties of ensuring transaction's immutability and facilitating accountable interactions, blockchains might enhance the overall guarantees and capabilities of serverless architectures. Therefore, in this work, we analyze how the blockchain technology and smart contracts fit into the serverless picture and derive a set of scenarios in which they act as different component types in serverless architectures. Furthermore, we formulate the implementation requirements that have to be fulfilled to successfully use blockchains and smart contracts in these scenarios. Finally, we investigate which existing technologies enable these scenarios, and analyze their readiness and suitability to fulfill the formulated requirements.