In Chap. 7 we study best approximation problems in a general Banach space. It is well known that best approximation problems have solutions only under certain assumptions on the space X. In view of the Lau-Konjagin result these assumptions cannot be removed. On the other hand, many generic results in nonlinear functional analysis hold in any Banach space. Therefore the following natural question arises: can generic results for best approximation problems be obtained in general Banach spaces? In this chapter we answer this question in the affirmative. To this end, we consider a new framework. The main feature of this new framework is that a best approximation problem is determined by a pair consisting of a point and a closed (convex) subset of a Banach space. We consider the complete metric space of such pairs equipped with a natural complete metric and show that for most (in the sense of Baire category) pairs the corresponding best approximation problem has a unique solution. We also provide some generalizations and extensions of this result.