T cells are integral components of the adaptive immune system, and their responses are mediated by unique T cell receptors (TCR) that recognize specific antigens from a variety of biological contexts. As a result, analyzing the T cell repertoire offers a better understanding of immune responses and of diseases like cancer. Next generation sequencing technologies have greatly enabled the high-throughput analysis of the TCR repertoire. Based on our extensive experience in the field from the past decade, we provide an overview of TCR sequencing, from the initial library preparation steps to sequencing and analysis methods and finally to functional validation techniques. With regards to data analysis, we detail important TCR repertoire metrics and present several computational tools for predicting antigen specificity. Finally, we highlight important applications of TCR sequencing and repertoire analysis to understanding tumor biology and developing cancer immunotherapies.