The rule is short: an asylum application must generally be filed within one year of the applicant's last arrival in the United States. The consequences of missing it are not short, because a late application is barred from asylum even when the underlying fear is genuine.
Why the date is not always obvious
The clock runs from the last arrival, which is not always the date someone remembers. It is also measured against the filing date, not the date you contacted a lawyer, not the date you gathered documents, and not the date an appointment was available. If you are close to the deadline, filing an application that can be supplemented later is usually better than a complete application filed late.
The exceptions
There are two, and both have to be established with evidence. Changed circumstances materially affecting eligibility, such as a shift in conditions in the home country, a change in the applicant's own situation, or new activity that creates risk. Extraordinary circumstances relating to the delay, such as serious illness, a legal disability including being a minor, ineffective assistance of counsel, or maintaining lawful status until shortly before filing.
Where an exception applies, the application still has to be filed within a reasonable period given those circumstances. Months of further delay after the reason for delay ends can sink an otherwise good claim.
Withholding and the Convention Against Torture
Missing the deadline does not necessarily end every protection. Withholding of removal and protection under the Convention Against Torture have no one-year filing bar, but they carry a higher standard of proof and give less: no path to a green card, no derivative status for family, and travel consequences that asylum does not have.
What matters most in practice
Asylum cases are decided on credibility and corroboration. Consistency between what you say at the border, what you write on the form, and what you testify to later is the spine of the case, which is why an application put together in a rush by someone who does not know the standards can cause damage that is difficult to repair.
If you are approaching one year in the United States and think you may have a claim, that is this week's problem, not next month's.