  In this thesis we give two applications of Ayoub's motivic nearby cycles
functor: First we give a generalization of Grothendieck's classical local
monodromy theorem. In the classical setup we show that the inertia group acts
quasi-unipotently on the \'etale cohomology of sheaves 'coming from motives'.
Second we study the notion of universal local acyclicity for motives and show
that for \'etale motives universal local acyclicity over an excellent 1-
dimensional regular base scheme is detected by the motivic nearby cycles
functor. Along the way we prove properties of the motivic nearby cycles functor
which might be of independent interest. In particular we show that with
rational coefficients the unipotent motivic nearby cycles functor is a direct
summand of the total motivic nearby cycles functor.
