NOTING UP involves examining how a case has been treated in subsequent cases to determine if it is still authoritative or "good law". This means checking if the relevant case has been reversed on appeal or overruled by a superior court in a later case.
You may also want to find other cases that have applied the law based on similar facts or later cases that have considered the case and may assist in terms of aiding judicial interpretation of the law.
In the United States the process of noting up is also known as Shepardizing. This term is also used in LexisNexis. In Westlaw it is referred to as KeyCite.