Structural heterogeneous OLAP data arise when several OLAP dimensions with different structure are mixed into a single OLAP dimension. In this chapter, we examine the problems encountered when handling structurally heterogeneity in OLAP and survey techniques that have been proposed to solve them. We show how to incorporate structural heterogeneity in the design of OLAP models. We explain why structural heterogeneity weakens aggregate navigation, the framework that guides users to formulate correct OLAP operations and systems to efficiently process them. We survey different techniques to deal with heterogeneity, including the modeling of heterogeneity by unbalanced dimensions, the solution proposed by Kimball, and the use of null elements to fix heterogeneity. Finally, we present a class of integrity constraints to model structural heterogeneity, called dimension constraints, introduced in previous work of the authors. We show the practical application of dimension constraints to support aggregate navigation and some of the aforementioned techniques for dealing with the problem.