  In the present paper we introduce and study the Lipschitz retractional
structure of metric spaces. This topic was motivated by the analogous
projectional structure of Banach spaces, a topic that has been thoroughly
investigated. The more general metric setting fits well with the currently
active theory of Lipschitz free spaces and spaces of Lipschitz functions. Among
our applications we show that the Lipschitz free space $\mathcal{F}(X)$ is a
Plichko space whenever $X$ is a Plichko Banach space. Our main results include
two examples of metric spaces. The first one $M$ contains two points $\{0,1\}$
such that no separable subset of $M$ containing these points is a Lipschitz
retract of $M$. The second example fails the analogous property for arbitrary
infinite density. Finally, we introduce the metric version of the concept of
locally complemented Banach subspace, and prove some metric analogues to the
linear theory.
