Discretionary review is the authority appellate courts have to decide which appeals they will consider from among the cases submitted to them. This offers the judiciary a filter on what types of cases are appealed, because judges have to consider in advance which cases will be accepted. The appeals court will then be able to decide substantive cases with the lowest opportunity cost. The opposite of discretionary review is any review mandated by statute, which guides appellate courts about what they can and cannot do during the review process.
The advantage to discretionary review is that it enables an appellate court to focus its limited resources on developing a coherent body of case law, or at least it is able to focus on making decisions in a consistent fashion (in jurisdictions where case law is not recognized). The disadvantage is that it reduces the ability of litigants to seek review of incorrect decisions of lower courts. However, the problem with allowing appeals of right through all appellate levels is that it encourages parties to exploit every technical error of each level of the court system as a basis for further review. Discretionary review forces parties to always concentrate their resources on persuading the trial court to get it right the first time around (rather than assuming an appellate court will "fix it later"), thus increasing the overall efficiency of the judicial system. Of course, it also leaves them at the mercy of the discretion of the trial court.
