The general rule is that the IRS has 10 years from the return due date for a return (April 15) or from the date the tax is assessed to collect. For a return filed after April 15, the tax assessment date will be the date the return is actually filed.
If the tax owed is from an audit, the 10 year period for the additional tax owed begins on the date that additional amount is assessed, after your audit has concluded.
There are a few exceptions to the general rule. The collection statute is also extended while the IRS is prevented from collecting through a bankruptcy stay (plus 6 months) or while administrative IRS remedies are being pursued, including innocent spouse relief requests, collection due process hearings, and offers in compromise. The collections statute may be tolled for additional days if the administrative relief is rejected while the time to appeal to Tax Court lapses, for example, an additional 30 days in the case of an offer in compromise and 90 days where innocent spouse relief is denied by an IRS determination letter.
In some cases the IRS, with the help of the Department of Justice, may bring suit in court to reduce a federal tax assessment to judgment which allows the IRS to collect on the liability beyond the ordinary ten-year limit. As with the assessment statute, a willful attempt to evade taxes allows for an unlimited collection statute insofar as the tax code allows for a suit to collect to be brought to collect the tax without the need for assessment.