One of the challenges faced by Wireless sensor networks (WSNs) is the issue of uncontrollable interference as the spectrum becomes congested due to the current proliferation of wireless devices. Cognitive radio (CR) emerged as one of the promising solutions to overcome the challenges while having the sensor nodes to access the licensed spectrum band. However, these sensors nodes consume huge amount of energy to accommodate the CR functionalities of sensing and switching between the spectrum bands. Consequently, an efficient mechanism is needed to enhance energy efficiency in the resulting cognitive radio sensor networks (CRSNs). Therefore, this paper surveys and analyses energy inefficiency challenges in the realm of WSN and CRSNs as well as some of the proposed approaches. The objective is to comprehend what has been done and how to improve the impeding challenges. We conducted the analysis on 11 related papers in the literature to analyze and identify the existing energy inefficiency challenges and the mechanisms to overcome them. The findings shows that energy inefficiency challenges is due to WSN performing CR capabilities thus, consuming a considerate amount of energy which causes the wireless sensor nodes energy to deplete incessantly. Moreover, several mechanisms have been proposed but more research need to be performed to find efficient solutions that are dynamic with technological advancements.