Cancer immunotherapy, focused on harnessing and empowering the immune system against tumours, has transformed modern oncology. One of the most promising avenues in development involves using genetically engineered T-cells to target cancer antigens via specific T-cell receptors (TCRs). TCRs have a naturally low affinity towards cancer-associated antigens, and therefore show scope for improvement. Here we describe approaches to procure TCRs with enhanced affinity and specificity towards cancer, using protein engineering or selection of natural TCRs from unadulterated repertoires. In particular, we discuss novel methods facilitating the targeting of tumour-specific mutations. Finally, we provide a prospective outlook on the potential development of novel, off-the-shelf immunotherapies by leveraging recent advances in genome editing.