The integration of cognitive radio and device-to-device (D2D) communication gives rise to Cognitive D2D (cD2D) communication, which offers numerous advantages, such as improved spectrum and energy efficiency, increased network throughput, and enhanced coverage. Although there are existing survey papers on cognitive networks and D2D communications, the topic of integrated cD2D communication has received limited attention. To bridge this gap in the literature, this paper presents a comprehensive survey of cD2D communication. We commence by introducing cD2D communication and highlighting the key research challenges in this field. Subsequently, we categorize the recent advancements in cD2D communications into eight major types of techniques and provide an in-depth review of the existing literature. Furthermore, we address several significant challenges associated with cD2D communications and discuss future applications that can benefit from this technology. Through our analysis, we aim to contribute to a deeper understanding of cD2D communication and provide insights into its potential for various domains.