Serverless computing has emerged as an attractive deployment option for cloud applications in recent times. The unique features of this computing model include, rapid auto-scaling, strong isolation, fine-grained billing options and access to a massive service ecosystem which autonomously handles resource management decisions. This model is increasingly being explored for deployments in geographically distributed edge and fog computing networks as well, due to these characteristics. Effective management of computing resources has always gained a lot of attention among researchers. The need to automate the entire process of resource provisioning, allocation, scheduling, monitoring and scaling, has resulted in the need for specialized focus on resource management under the serverless model. In this article, we identify the major aspects covering the broader concept of resource management in serverless environments and propose a taxonomy of elements which influence these aspects, encompassing characteristics of system design, workload attributes and stakeholder expectations. We take a holistic view on serverless environments deployed across edge, fog and cloud computing networks. We also analyse existing works discussing aspects of serverless resource management using this taxonomy. This article further identifies gaps in literature and highlights future research directions for improving capabilities of this computing model.