A formulary exception is a request for your plan to cover a clinically appropriate drug it does not otherwise cover. Under federal rules (45 CFR 156.122), non-grandfathered individual and small-employer insured plans, the ones that must cover essential health benefits, must have this process. You, someone you name, or your prescriber can make the request.
The standard request gets a decision within 72 hours of the plan receiving it. If approved, the plan covers the drug for the duration of the prescription, including refills. If your health could be seriously harmed by waiting, or you are already on a current course of treatment with a non-formulary drug, you can ask for an expedited review, with a decision within 24 hours.
If the plan denies the request, you can ask for review by an independent review organization. That decision is also due within 72 hours for a standard request and 24 hours for an expedited one. A state can accept its own appeal process in place of this one if it is at least as strict. Other plan types, such as large employer plans, may have different appeal rules, so read your plan documents.