We survey the recent research in the field of cake divisions and their procedures. The question is how to divide a cake among n players, so that a certain fairness is achieved, where players have individual measures on the cake, and each player only knows his own measure. The model has very wide applications, such as dividing up the property in an estate, and even in determining the border in an international dispute. We first review mathematical definitions of various concepts of fairness. Although the existence of fair divisions is proved under some mathematical conditions, their dividing procedures are not known for all cases. We summarize several existing division procedures and classify them according to their methods and purposes. Finally, we mention some related topics and describe possible future research directions.
