Clustered regularly interspaced short palindromic repeats (CRISPR) and CRISPR-associated proteins (Cas) constitute a multi-functional, constantly evolving immune system in bacteria and archaea cells. A heritable, molecular memory is generated of phage, plasmids, or other mobile genetic elements that attempt to attack the cell. This memory is used to recognize and interfere with subsequent invasions from the same genetic elements. This versatile prokaryotic tool has also been used to advance applications in biotechnology. Here we review a large body of CRISPR-Cas research to explore themes of evolution and selection, population dynamics, horizontal gene transfer, specific and cross-reactive interactions, cost and regulation, non-immunological CRISPR functions that boost host cell robustness, as well as applicable mechanisms for efficient and specific genetic engineering. We offer future directions that can be addressed by the physics community. Physical understanding of the CRISPR-Cas system will advance uses in biotechnology, such as developing cell lines and animal models, cell labeling and information storage, combatting antibiotic resistance, and human therapeutics.