Service systems often feature multiple classes of customers with different service needs and multiple pools of servers with different skillsets. How to efficiently match customers of different classes with servers of different skillsets is of great importance to the management of these systems. In this survey, we review works on skill-based routing in queues. We first summarize key insights on routing/scheduling policies developed in the literature. We then discuss complications brought by modern service operations management problems, particularly healthcare systems. These complications stimulate a growing body of literature on new modeling and analysis tools. Lastly, we provide additional numerical experiments to highlight the complex nature of a routing problem motivated from hospital patient-flow management, and provide some useful intuition to develop good skill-based routing policies in practice. Our goal is to provide a brief overview of the skill-based routing research landscape and to help generate interesting research ideas.