The minimisation of a smooth objective function subject to a matrix rank constraint can sometimes be very effectively solved by methods from Riemannian optimisation. This is for instance the case with the low-rank matrix completion problem or the solution of PDEs on square domains like the Lyapunov equation. However, the theory of Riemannian optimisation leaves some questions unanswered regarding the practical application of such algorithms. I will focus on two such questions. The first is how the metric has a significant impact on the convergence of the numerical methods. This is related to how Newton’s method can be seen as a variable metric in numerical optimisation and to general preconditioning techniques. The second topic is rank adaptivity. In rank-constrained optimisation, one does typically not know the rank a priori but may be searching for the smallest rank satisfying a certain criterion, like a small residual. I will explain how the geometry of the tangent cone of the variety of matrices of bounded rank can be incorporated so as to obtain rank adaptive algorithms that stay true to the manifold philosophy.