The emerging serverless computing paradigm has attracted attention from both academia and industry. This paradigm brings benefits such as less operational complexity, a pay-as-you-go pricing model, and an auto-scaling feature. The paradigm opens up new opportunities and challenges for cloud application developers. In this article, we present a comprehensive overview of the past development as well as the recent advances in research areas related to serverless computing. First, we survey serverless applications introduced in the literature. We categorize applications in eight domains and separately discuss the objectives and the viability of the serverless paradigm along with challenges in each of those domains. We then classify those challenges into nine topics and survey the proposed solutions. Finally, we present the areas that need further attention from the research community and identify open problems.