The known geometric algorithms for discrete subgroups of $\mathrm{SL}(n,\R)$ come primarily in two forms, both requiring the subgroup to be ``geometrically nice.'' While the ultimate definition of ``niceness'' is, at this point, very much unclear, the known forms include (a) {\em the traditional geometric finiteness} using a finitely-sided fundamental domain (using either an invariant Riemannian metric or Selberg's 2-point invariant) in the associated symmetric space, (b) the relatively recent notion of {\em Anosov subgroups}. Both definitions allow for geometric local-to-global principles, which, in turn, make computations with such discrete subgroups possible. The lectures will describe theses two concepts, the local-to-global principles and the geometric algorithms.