Abstract: Neutron stars may have a core of deconfined quark matter. If the quark-hadron transition is of first order, the interface between the quark core and the surrounding nuclear matter either has a sharp density jump or is composed of mixed phases, for instance quark matter bubbles immersed in nuclear matter. I will briefly review astrophysical implications and theoretical challenges and will report on recent results for the surface tension, which is important to estimate existence and thickness of the mixed phase layer.