Passive systems are fundamental for the safe development of Nuclear Power Plant (NPP) technology. The accurate assessment of their reliability is crucial for their use in the nuclear industry. In this paper, we present a review of the approaches and procedures for the reliability assessment of passive systems. We complete the work by discussing the pending open issues, in particular with respect to the need of novel sensitivity analysis methods, the role of empirical modelling and the integration of passive safety systems assessment in the (static/dynamic) Probabilistic Safety Assessment (PSA) framework.