This talk consists of two different topics related to Nahm's equations. In the first part, I will explain how concatenation of solutions to Nahm's equations on compact intervals give groupoid structures, in a manner analogous to the fundamental groupoid of a topological space. In the second part, I will draw analogies between the moduli space of solutions to Nahm's equations on an open interval with fixed poles at the endpoints and the moduli space of Higgs bundles over a curve. Both spaces are hyperkähler manifolds and have fibrations onto vector spaces making them completely integrable systems. Moreover, the mirror symmetry program for moduli spaces of Higgs bundles has many features which have analogues in this Nahm moduli space, such as dual fibrations and non-trivial branes coming from involutions.