In energy harvesting cognitive radio sensor networks(EHCRSNs), energy harvesting supplies continual energy to eliminate the limitation of limit-battery sensor, while cognitive radio mitigates the scarcity of spectrum resource. Hence, the operation of EHCRSNs can be continually and effectively executed. However, due to the dynamic and stochastic property of the energy harvesting progress and the available spectrum, there are some significant challenges in the area of network resource management of EHCRSNs. This paper will firstly introduce the background of EHCRSNs. Then, the research on EHCRSNs is systematically summarized and discussed. At last, we point out limitations of these studies and possible future research directions.