In the design of novel nuclear reactors active systems are replaced by passive ones in order to reduce the risk of failure. For that reason natural circulation is being considered as the primary cooling mechanism in next generation nuclear reactor designs such as the natural circulation boiling water reactor (BWR). In such a reactor, however, the flow is not a controlled parameter but is dependent on the power. As a result, the dynamical behavior significantly differs from that in conventional forced circulation BWRs. For that reason, predicting the stability characteristics of these reactors has to be carefully studied. In this work, a number of open issues are investigated regarding the stability of natural circulation BWRs (e.g. margins to instabilities at rated conditions, interaction between the thermal-hydraulics and the neutronics, and the occurrence of flashing induced instabilities) with a strong emphasis on experimental evidence.