CRISPR-Cas adaptive immune systems are widespread among bacteria and archaea. Recent studies have shown that these systems have minimal long-term evolutionary effects in limiting horizontal gene transfer. This suggests that the ability to evade CRISPR-Cas immunity must also be widespread in phages and other mobile genetic elements. In this Progress article, we discuss recent discoveries that highlight how phages inactivate CRISPR-Cas systems by using anti-CRISPR proteins, and we outline evolutionary and biotechnological implications of their activity.