Geometric and canonical triangulations of highly twisted knots

It is conjectured that every cusped hyperbolic 3-manifold admits a geometric triangulation, that is, it can be decomposed into positive volume ideal hyperbolic tetrahedra. In this thesis, we show that sufficiently highly twisted knots admit a geometric triangulation. In addition, by extending work of Gueritaud and Schleimer, we give quantified versions of this result for several infinite families of examples. Further, we show that many of these triangulations are in fact canonical.