Canon law is applied through a real court system, and its structure is worth setting out because most discussion of it, particularly around marriage annulment, assumes a courtroom without describing one.
Each diocese maintains a tribunal, headed by a judicial vicar appointed by the bishop, staffed by trained canon lawyers who serve as judges, defenders of the bond, and advocates for the parties. The most common case type by far is the declaration of nullity, a finding that a marriage, though it appears valid, lacked some element canon law requires for validity from the outset, such as full consent, the capacity to consent, or the intention to marry permanently and exclusively; a declaration of nullity is not a divorce, since it holds that no valid marriage existed rather than that an existing one is dissolved.
Cases proceed through instances: a first-instance tribunal decision, if affirmative, historically required automatic review by a second-instance tribunal before taking effect, a safeguard Pope Francis's 2015 reform Mitis Iudex Dominus Iesus relaxed by allowing a single affirmative decision to become final if neither party appeals. Above the diocesan level sits the Roman Rota, the ordinary appellate tribunal of the Holy See, whose accumulated decisions (jurisprudence) function similarly to case law in guiding how later tribunals interpret the Code's grounds for nullity.
Separately, the Congregation for the Doctrine of the Faith (renamed the Dicastery for the Doctrine of the Faith in 2022) handles the gravest penal cases, including clergy sexual abuse, reserved to it since 2001 specifically because diocesan-level handling of such cases had proven so inadequate.