Abstract: 2D materials can be stacked in many ways allowing for a large range of tuning parameters to control electronic properties. One of these parameters includes a relative twist angle in plane between the various layers. While individual layers may exhibit periodicity, the global ensemble has no periodicity, and is then called incommensurate. Further, different species of 2D materials naturally have different periodicities, and become incommensurate regardless of choice of angle. Incommensurate 2D materials with two or more similar periodicities form large moiré patterns resulting in exotic quantum phases including for twisted bilayer graphene correlated insulation, unconventional superconductivity, and the fractional quantum Hall effect. To understand and predict properties of moiré materials, accurate ab initio models derived from first principle physics are necessary. In this talk, we will discuss how momentum space techniques can be used to compute electronic observables and quasi-band structure for ab initio tight-binding models with various geometry complexities including double-incommensurate trilayers and mechanically relaxed twisted bilayers. We also discuss how this formulation can derive periodic continuum models including the Bistritzer-MacDonald model.