Joint work with A. Sarti. Singular K3 surfaces are the K3 surfaces with maximal Picard number, namely 20. I will explain how to construct families of K3 surfaces with big Picard number using invariants of finite complex reflection groups of rank 4, each family containing some singular ones. This extends earlier work of Barth-Sarti for two reasons: firstly, we obtain much more examples by considering all reflection groups of rank 4 and, secondly, our proofs involve more theory of complex reflection groups and avoids as much as possible (but not completely) a case-by-case analysis.