  In this paper we propose to use a relative variant of the notion of the
\'{e}tale homotopy type of an algebraic variety in order to study the existence
of rational points on it. In particular, we use an appropriate notion of
homotopy fixed points in order to construct obstructions to the local-global
principle. The main results in this paper are the connections between these
obstructions and the classical obstructions, such as the Brauer-Manin, the
\'{e}tale-Brauer and certain descent obstructions. These connections allow one
to understand the various classical obstructions in a unified framework.
