My answer will only be partial, i.e. about serial killers.
The FBI "Crime Classification Manual" roughly divide serial killers in 3 categories: organized, disorganized and mixed.
While the organized serial killers are usually smart, plan their crimes beforehand, follow a precise and thorough ritual (and especially, use equipment they brought with them) and feel no regrets, the disorganized serial killer obey an uncontrollable urge, use weapons found on the scene and usually have regrets in the aftermath.
Because of afterthoughts, like regrets or fear to be discovered, the disorganized serial killers can return to the crime scene, hiding in the crowd. And an investigation method is to take pictures of the crowd on each crime scene, in order to search for persons appearing on several ones.
Quote of the indicated book, 2nd edition, page 220:
Postoffense behavior exhibited may be a change in eating habits and
drinking habits (more alcohol consumption) and nervousness. He may
also have an inappropriate interest in the crime, for example, by
frequently engaging in conversation about it. Disorganized behavior
may be evident in victim selection, crime scene, and forensics due to
youthfulness, drug or alcohol impairment, external stressors (for
example, fear of discovery), or lack of criminal sophistication.