A checked bag that doesn’t turn up is usually declared lost after a period (commonly 21 days). On an international flight the Montreal Convention makes the airline liable for the value of the bag and its contents, up to about 1,519 SDR (~US$2,100 / €1,800) per passenger.

[Your name / address / email / phone]
[Date]
[Airline] — Baggage Claims

Re: Lost baggage claim — Montreal Convention 1999, Article 17(2)
    Flight [number] — [origin] to [destination] — [date]
    PIR / file reference: [____]   ·   Booking: [PNR]
    Bag tag number(s): [____]

Dear Sir or Madam,

My checked bag on flight [number] on [date] (PIR [____]) was not
delivered and has now been [declared lost / not located after [X] days].

Under Article 17(2) of the Montreal Convention, the carrier is liable for
the loss of checked baggage up to the per-passenger limit (currently
1,519 SDR, effective 28 December 2024). I claim for the bag and its
contents as itemized below (proofs of purchase/photos enclosed where
available):

    [Item — description] .............. [value]
    [Item — description] .............. [value]
    ----------------------------------------------
    TOTAL CLAIMED ..................... [currency + amount]

Please settle this claim, up to the applicable limit, within [21] days.

Yours faithfully,
[Signature / printed name]

Notes

Itemize honestly with values and proof. List contents with realistic replacement values; attach receipts, bank records, or photos where you can. Airlines may apply depreciation to used items.
The limit is per passenger, not per bag. 1,519 SDR is the cap unless you made a special declaration of higher value at check-in and paid a fee (Article 22(2)).
Deadlines: there’s no fixed “lost” complaint window like the 7/21-day damage/delay rules, but file promptly and note the 2-year limit to sue.
High-value items (jewelry, electronics, cash) are often excluded or limited by the airline’s conditions of carriage and may exceed the cap — travel insurance or a homeowner’s policy may cover the gap.

Don’t accept a token “lost bag” flat fee as full settlement. Airlines sometimes offer a small fixed sum. Under the Montreal Convention you can claim your actual itemized loss up to ~1,519 SDR. Put your itemized claim in writing and ask them to justify any lower offer. US domestic? See US passenger rights ($4,700 cap).

Lost baggage claim letter (Montreal Convention)