Advances in forensic techniques have expanded the temporal horizon of criminal investigations, facilitating investigation of historic crimes that would previously have been considered unsolvable. Public enthusiasm for pursuing historic crimes is exemplified by recent high-profile trials of celebrities accused of historic sexual offences. These circumstances give new urgency to the question of how we should decide which historic offences to investigate. A satisfactory answer must take into account the ways in which the passage of time can erode the benefits of (...) criminal investigation, the costs associated with investigating old crimes, and the need to prioritize investigations in the face of limited police resources. This article emphasizes the first of these factors. It begins by considering the moral goals of a criminal justice system and the contribution of criminal investigations to the achievement of these goals, distinguishing between contributions that depend on further steps in the criminal justice process, such as prosecution and punishment, and contributions that can have value independently of these further steps. Using this important distinction, the article then examines a range of factors that relate the passage of time to criminal justice goals, including the seriousness of the crime; deterioration of evidence; death of the offender, victim and others affected by the crime; and diminished psychological connectedness between those affected by the crime and their current selves. While the range and non-uniformity of relevant factors preclude a simple answer to the question of when historic crimes should be investigated and call instead for case-by-case assessment, we find that the analysis does support some general conclusions that can guide such an assessment. (shrink)