In this work we review our new methods to computer generate amorphous atomic topologies of several binary alloys: SiH, SiN, CN; binary systems based on group IV elements like SiC; the GeSe 2 chalcogenide; aluminum-based systems: AlN and AlSi, and the CuZr amorphous alloy. We use an ab initio approach based on density functionals and computationally thermally-randomized periodically-continued cells with at least 108 atoms. The computational thermal process to generate the amorphous alloys is the undermelt-quench approach, or one of its variants, that consists in linearly heating the samples to just below their melting (or liquidus) temperatures, and then linearly cooling them afterwards. These processes are carried out from initial crystalline conditions using short and long time steps. We find that a step four-times the default time step is adequate for most of the simulations. Radial distribution functions (partial and total) are calculated and compared whenever possible with experimental results, and the agreement is very good. For some materials we report studies of the effect of the topological disorder on their electronic and vibrational densities of states and on their optical properties.