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In this Colloquium, I describe some current frontiers in the physics of semiconducting amorphous materials and glasses, including a short, but self-contained discussion of techniques for creating computer models, among them the quench from the melt method, the Activation-Relaxation Technique, the decorate and relax method, and the experimentally constrained molecular relaxation scheme. A representative study of an interesting and important glass (amorphous GeSe₃:Ag) is provided. This material is a fast-ion conductor and a serious candidate to replace current FLASH memory. Next, I discuss the effects of topological disorder on electronic states. By computing the decay of the density matrix in real space, and also computing well-localized Wannier functions, we close with a quantitative discussion of Kohn’s Principle of Nearsightedness in amorphous silicon.