While the photographing of criminals began in the 1840s shortly after the invention of photography, it was not until 1888 that French police officer Alphonse Bertillon standardized the process.

Mug shots, which were typically taken after a person was arrested, allowed law enforcement to have a photographic record of an arrested individual to allow for identification purposes by victims, the public and investigators.

Alphonse Bertillon (24 April 1853 – 13 February 1914) was a French police officer and biometrics researcher who applied the anthropological technique of anthropometry to law enforcement creating an identification system based on physical measurements. Anthropometry was the first scientific system used by police to identify criminals. Before that time, criminals could only be identified by name or photograph. The method was eventually supplanted by fingerprinting. [source]

Bertillon was also a witness for the prosecution in the Dreyfus affair in 1894 and again in 1899. He testified as a handwriting expert and claimed that Alfred Dreyfus had written the incriminating document (known as the “bordereau”). However, he was not a handwriting expert, and his convoluted and flawed evidence was a significant contributing factor to one of the most infamous miscarriages of justice – the condemnation of the innocent Dreyfus to life imprisonment on Devil’s Island. [source]