Function-as-a-Service (FaaS) is a novel cloud service model allowing to develop fine-grained, provider-managed cloud applications. In this work, we investigate which challenges motivate researchers to introduce or enhance FaaS platforms and tools. We use a systematic mapping study method to collect and analyze the relevant scientific literature, which helps us answering the three clearly-defined research questions. We design our study using well-established guidelines and systematically apply it to 62 selected publications. The collected and synthesized data provides useful insights into the main challenges that motivate researchers to work on this topic and can be helpful in identifying research gaps for future research.