Notice of Appeal
Let's pretend for a moment that you file an application and things just don't go all that smoothly. You keep receiving your Office actions and desperately try to correct all that is wrong, but the examiner sends you a Final rejection anyway. After your claims have been rejected at least twice, you may appeal from the decision of the examiner.

The first step in this time consuming and expensive process is to send in a Notice of Appeal. The Notice of Appeal must be filed within the period for reply set in the last Office action, otherwise, your application will become abandoned. The Notice of Appeal really only serves as a Notice to the PTO that an appeal will be filed. Therefore, it merely needs to refer to the appropriate application and state that an appeal will be filed. Once the Notice of Appeal is sent in, the applicant will only have two months to file the Appeal Brief.

Appeal Brief
The Appeal brief is an interesting and complex document. The main point of the brief is to state the reasons why the claims should not be rejected. It must present arguments responsive to every ground of rejection stated by the examiner in the Office action from which the appeal has been taken.  It's up to the appellant to present arguments as to why each rejected claim is patentable.

From here, the examiner may address the Appeal Brief. If the examiner chooses to reply, then the appellant may file a reply brief, rebutting the examiner's response.

If the appeal continues, it will be the Patent Trial and Appeal Board (PTAB) who determines the fate of the application. The Board may side with the appellant and decide that the examiner was wrong in rejecting the claims. Alternately, they may side with the examiner and agree that the claims in fact, should be rejected.

In addition, the Board may also find new grounds for a rejection. If the Board happens to find a new rejection, the applicant may request that the examiner reconsider the matter. The applicant may also request a rehearing by the Board within the two months following the decision by the Board.

If the Board decides that no claims stand allowed, then the proceedings are considered terminated and the application will be abandoned. If at least one allowed claim remains in the application (rejections are always made on a claim by claim basis), then the application will not be abandoned, but may issue as a patent.