Cognitive radio (CR), as a concept based on the ability to detect and share the unutilised spectrum, has been envisioned as a promising candidate to improve the efficiency of frequency spectrum assignments. For the realisation of the CR concept, energy detection (ED), as one of the available spectrum sensing methods, is broadly considered because of its low computational complexity and implementation costs. Due to the vast usage of the orthogonal frequency division multiplexing (OFDM) technique in contemporary communication systems, the ED of OFDM signals in the CR networks has become important for practical realisation. Since the ED accuracy of the OFDM signals can be improved by the sensing threshold adaptation, this paper surveys the impact of noise variations and dynamic threshold (DT) adaptation on the ED performance of OFDM signals. Analyses were performed by the simulation of the ED related to OFDM signals transmitted in the margin or rate adaptive and combined margin and rate adaptive OFDM systems. The results obtained through extensive simulations provide fundamental insights into how different factors, including the transmission power, the signal to noise ratio, the false alarm probability and the sample quantity, affect the ED efficiency. Comprehensive analyses of the obtained results indicate the main ED weaknesses and how the appropriate selection of analysed factors can enhance the ED processes for different OFDM systems. The observed ED weaknesses were further thoroughly surveyed, and the open issues and challenges related to the enhancement of the main ED limitations have been elaborated. The presented survey results can serve as a basis for the improvement of a broadly accepted ED method in CR networks.