In both tort and criminal law, strict liability exists when a defendant is liable for committing an action, regardless of what his/her intent or mental state was when committing the action. In criminal law, possession crimes and statutory rape are both examples of strict liability offenses.
Strict Liability As Applied to Criminal Law
In criminal law, strict liability is generally limited to minor offenses. Criminal law classifies strict liability as one of five possible mentes reae (mental states) that a defendant may have in pursuit of the crime. The other four are "acting knowingly," "acting purposely," "acting with recklessness," and "acting with negligence." The mens rea of strict liability typically results in more lenient punishments than the other four mentes reae. Typically in criminal law, the defendant's awareness of what he is doing would not negate a strict liability mens rea (for example, being in possession of drugs will typically result in criminal liability, regardless of whether the defendant knows that he is in possession of the drugs).
Strict Liability As Applied to Tort Law
In tort law, there are two broad categories of activities for which a plaintiff may be held strictly liable - possession of certain animals and abnormally dangerous activities. Additionally, in the area of torts known as products liability, there is a sub-category known as strict products liability which applies when a defective product for which an appropriate defendant holds responsibility causes injury to an appropriate plaintiff.
The classification of strict liability has not been without controversy. Some scholars oppose the concept for reasons commonly related to the unfairness of a defendant being held liable for something unrelated to the defendant's intentions (or lack thereof). Others support the classification, with some reasoning that the more lenient punishments which accompany strict liability offenses mitigate the potential unfairness related to the classification.
For further reading on the topic, see this William & Mary Law Review note; see also this Yale Law School Legal Scholarship Repository article; see also this Michigan Law Review note.