About 20 years ago, DNA sequences were separately described from the quagga (a type of zebra) and an ancient Egyptian individual. What made these DNA sequences exceptional was that they were derived from 140- and 2400-year-old specimens. However, ancient DNA research, defined broadly as the retrieval of DNA sequences from museum specimens, archaeological finds, fossil remains, and other unusual sources of DNA, only really became feasible with the advent of techniques for the enzymatic amplification of specific DNA sequences. Today, reports of analyses of specimens hundreds, thousands, and even millions of years old are almost commonplace. But can all these results be believed? In this paper, we critically assess the state of ancient DNA research. In particular, we discuss the precautions and criteria necessary to ascertain to the greatest extent possible that results represent authentic ancient DNA sequences. We also highlight some significant results and areas of promising future research.