The ASPECT code (short for "Advanced Solver for Problems in Earth ConvecTion") solves problems relating to the motion of material, energy, and composition in both the Earth crust and the mantle. This is described by a coupled system that involves instantaneous Stokes flow, the advection and diffusion of a temperature field, and the advection and reaction of chemical compositions or other quantities. It can also simulateously solve for the deformation of the Earth surface, as well as advect particles with the flow field. The resulting time stepping scheme is diverse, but for the most part only uses home-grown time steppers that, for historical reasons, are not well integrated. I will discuss what we do and why, as well as what we do not do and why not. I will also discuss what I think better solutions could be.