Criminal investigation is the process of determining the existence of a crime, collecting evidence, and identifying suspects. It may include the interrogation of suspects, but arrest is typically a legally separate process. Depending on the jurisdiction, it may be completely a police function, or may also involve investigators from a prosecutor's office. Police that specialize in investigating complex crimes are detectives.
As opposed to techniques in intelligence collection, the methods involved are assumed to be restricted to those that will produce evidence admissible in the relevant court. For example, in general Western criminal investigation, there must be a prior warrant for searches and wiretaps.
Interrogation, to be admissible, may require warnings to the suspect, the presence of an attorney, and avoidance of the use of certain methods.