Claims process has many twists and turns, generally speaking

Whose duty is it to obtain compensation in a motor vehicle accident when both vehicles are insured? Are there any time limits within which insurers must operate? What are some of the things that determine when an insurer will drop a case when there is no response from the other insurer? I get hundreds of emails and scores of text/telephone messages each week. Few of them are about risks or insurance. Many of the persons who contact me have a particular problem for which they want specific help or information to resolve.