  We review a geometric approach to proving absolutely continuous (ac) spectrum
for random and deterministic Schr\"odinger operators developed in
\cite{FHS1,FHS2,FHS3,FHS4}. We study decaying potentials in one dimension and
present a simplified proof of ac spectrum of the Anderson model on trees. The
latter implies ac spectrum for a percolation model on trees. Finally, we
introduce certain loop tree models which lead to some interesting open
problems.
