Tree convex sets refer to a collection of sets such that each set in the collection is a subtree of a tree whose nodes are the elements of these sets. They extend the concept of row convex sets each of which is an interval over a total ordering of the elements of those sets. They have been applied to identify tractable Constraint Satisfaction Problems and Combinatorial Auction Problems. Recently, polynomial algorithms have been proposed to recognize tree convex sets. In this paper, we review the materials that are the key to a linear recognition algorithm.