Each airline has a Public Relations office that will accept and handle your complaint regarding service. Generally you can email your complaint via the airline website or the website will have an address for you to mail a letter.
Lost baggage should be handled at the local airline ticket counter or baggage service office immediately after your flight has arrived.
Delta Baggage Claim: 208-529-8003
United Baggage Claim: 208-529-8003
Allegiant Baggage Claim: 866-719-3910
Alaska Air Baggage Claim: 877-815-8253
American Air Baggage Claim: Online