We define locally conformally Kähler (lcK) spaces with possible singularities and talk about a few recent results obtained on them, chiefly an equivalent description in terms of their universal cover and the existence of a type of Vaisman Theorem about the compatibility of an lcK and a Kähler structure. We then define generalized lcK metrics and use them to show that this new class of spaces is stable under modifications. This is a joint work with Ovidiu Preda.