When a compact Lie group acts freely and in a Hamiltonian way on a symplectic manifold, the Marsden-Weinstein theorem says that the reduced space is a smooth symplectic manifold. If we drop the freeness assumption, the reduced space might be singular, but Sjamaar-Lerman (1991) showed that it can still be partitioned into smooth symplectic manifolds which "fit together nicely" in the sense that they form a stratification. In hyperkähler geometry, there is an analogue of symplectic reduction which has been a very important tool for constructing new examples of these special manifolds. In the first part of this talk, I will explain how Sjamaar-Lerman's results can be extended to this setting, namely, hyperkähler quotients by non-free actions are stratified spaces whose strata are hyperkähler. In the second part, I will review the notion of Nahm's equations and use them to give interesting examples of such stratified hyperkähler spaces.