In numerical approximation of PDEs, the design of a numerical method is justified by a priori error estimates, while its actual behavior is controlled by (and possibly steered by) a posteriori error estimates. Besides, to practically obtain the numerical approximation, a suitable solver for the associated system of nonlinear or linear algebraic equations is needed. Numerical parameters (such as mesh size and regularity, polynomial degree, or amount of stabilization) and PDE parameters (such as mutual ratios of advective, reactive, and diffusive effects, wavenumber, strength of the nonlinearity, or final time size for evolution problems) enter the numerical analysis and can affect the actual performance of such methods. When the analysis and/or the practical performance of these methods is insensitive to these parameters, we speak of robustness. The subject of this minisymposium is robustness in a priori and a posteriori error estimates and in (iterative) algebraic solvers.