The Statute of Limitations is a limit on how long a legal action can be taken. Once the requisite time passes the legal action (prosecution, lawsuit, whatever) is no longer allowed. The running of a statute of limitations is a complete defense to a crime in most circumstances. We have requirements for timeliness in most cases because it is considered unfair to prosecute some crimes after a very long period of time has passed because it reduces the ability of the defendant to defend themselves. However...
Not everything has a time limit. Murder, for instance, does not have a statute of limitations. You can be prosecuted for as long as you are alive if you are suspected of murder. And some things have differing ways of calculating the time limit and under some circumstances the time limit may stop running for a while and then continue running again once the circumstance is resolved.
The timeliness requirement for starting a prosecution it is generally satisfied when the case is filed if the statute has not already run on it, but if the case is dismissed then it still runs from the original point. As an example, if the statute of limitations on a case is three years and the case is prosecuted and then dismissed it can still be reopened if it's been less than three years since the crime was committed.
The various limitations in Oklahoma are set out in Sections 151, 152, and 153 of Title 22 of the Oklahoma Statutes (22 O.S. §151-153) and briefly they follow.
Murder -- No time limit
Various Crimes that Amount to Stealing from the State or Local Government -- 7 years after the discovery of the crime
Stealing from Vulnerable Adults -- 5 years after the discovery of the crime
Sex Crimes Against Children -- by the 45th birthday of the victim *
Sex Crimes Against Adults -- 12 years from the discovery of the crime *
* but if DNA is saved and can be tested then prosecution has no time limit, but must commence within 3 years of the discovery of a suspect through DNA testing
Bogus Checks -- 5 years after the commission of the crime
Fraud and Workers' Comp Fraud -- within 3 years after the discovery of the crime, but no longer than 7 years after the commission of it in any case
Solicitation for Murder -- within 7 years after the discovery of the crime
Accessory to any offense -- same as the offense
Arson -- 7 years
For any offense in which a deadly weapon is used in the commission of the offense -- at least 7 years if not otherwise already longer
All other offenses not already laid out here -- 3 years
If the defendant is out of state when the crime is committed then the limitation time that they're out of state doesn't count and no time that the defendant is not a resident or habitually in the state counts.