Abstract: Incommensurate 2D materials with two similar periodicities form large moiré patterns resulting in unique electronic properties including correlated insulators and superconductors. Before studying correlated effects, a thorough understanding of the single-particle picture is critical as a reduced single-particle basis is key for constructing two-body models. The most popular approximate models are the continuum models.  In this work, we analyze the accuracy of continuum models relative to the more fundamental tight-binding models (including ab initio tight-binding). We show continuum models such as the popular Bistritzer-MacDonald model can be realized as careful Taylor expansions of a momentum space approximation of tight-binding, and discuss accuracy and the effect on the band structure of various order expansions in the setting of twisted bilayer graphene. The momentum space and continuum models both yield candidate single-particle bases for many-body models.