Over the past decades, adoptive transfer of T cells has revolutionized cancer immunotherapy. In particular, T-cell receptor (TCR) engineering of T cells has marked important milestones in developing more precise and personalized cancer immunotherapies. However, to get the most benefit out of this approach, understanding the role that TCR affinity, avidity, and functional avidity play on how TCRs and T cells function in the context of tumor-associated antigen (TAA) recognition is vital to keep generating improved adoptive T-cell therapies. Aside from TCR-related parameters, other critical factors that govern T-cell activation are the effect of TCR co-receptors on TCR-peptide-major histocompatibility complex (pMHC) stabilization and TCR signaling, tumor epitope density, and TCR expression levels in TCR-engineered T cells. In this review, we describe the key aspects governing TCR specificity, T-cell activation, and how these concepts can be applied to cancer-specific TCR redirection of T cells.