The present issue intends to provide an exposition of very recent topics and results in thequalitative study of nonlinear elliptic equations or systems such as, e.g., existence, multiplicity,and comparison principles. Emphasis is put on variational techniques, combined with topologicalarguments and sub-super-solution methods, in both a smooth and non-smooth framework.  The collected papers investigate a wide range of questions. Let us mention for instance multiple solutions to ellipticequations and systems in bounded or unbounded domains, sub-super-solutions of elliptic problems whoserelevant energy functionals can be non-differentiable, singular elliptic equations, asymptoticallycritical problems on higher dimensional spheres, local $C^1$-minimizers versus local $W^{1,p}$-minimizers.  Each contribution is original and thoroughly reviewed.