The primary theme of this thesis is to extend various classical techniques and spectral results regarding 1-dimensional Schrödinger operators with locally integrable potentials to the more general setting of distributional potentials which are locally in the Sobolev space H^{-1}. We will start by reviewing the classical spectral theoretical framework along with relevant results obtained therein. Next, we proceed to establish the corresponding framework in the distributional setting, and recover Last–Simon-type description of the absolutely continuous spectrum and sufficient conditions for different spectral types. In the last chapter, we focus on potentials which are decaying in a locally H^{−1} sense. In particular, we prove a spectral transition between short-range and long-range in the class of sparse distributional potentials, and we establish WKB-type asymptotic behavior of eigenfunctions and spectral properties for locally H^{−1} potentials whose decay rate is between L^1 and L^2.