Gene drives are selfish genetic elements that use a variety of mechanisms to ensure they are transmitted to subsequent generations at greater than expected frequencies. Synthetic gene drives based on the clustered regularly interspersed palindromic repeats (CRISPR) genome editing system have been proposed as a way to alter the genetic characteristics of natural populations of organisms relevant to the goals of public health, conservation, and agriculture. Here, we review the principles and potential applications of CRISPR drives, as well as means proposed to prevent their uncontrolled spread. We also focus on recent work suggesting that factors such as natural genetic variation and inbreeding may represent substantial impediments to the propagation of CRISPR drives.