In this survey we report on some recent results related to various singular phenomena arising in the study of some classes of nonlinear elliptic equations.We establish qualitative results on the existence, nonexistence or the uniqueness of solutions and we focus on the following types of problems: (i) blow-up boundary solutions of logistic equations; (ii) Lane–Emden– Fowler equations with singular nonlinearities and subquadratic convection term.We