Cell-free (CF) architecture and full-duplex (FD) communication are leading candidates for next-generation wireless networks. The CF framework removes cell boundaries in traditional cell-based systems, thereby mitigating inter-cell interference and improving coverage probability. In contrast, FD communication allows simultaneous transmission and reception on the same frequency-time resources, effectively doubling the spectral efficiency (SE). The integration of these technologies, known as CF FD communication, leverages the advantages of both approaches to enhance the spectral and energy efficiency in wireless networks. CF FD communication is particularly promising due to the low-power and cost-effective FD-enabled access points (APs), which are ideal for short-range transmissions between APs and users. Despite its potential, a comprehensive survey or tutorial on CF FD communication has been notably absent. This paper aims to address this gap in the literature. It begins with an overview of FD communication fundamentals, self-interference cancellation techniques, and CF technology principles, including their implications for current wireless networks. The discussion then moves to the integration and compatibility of CF and FD technologies, focusing on channel estimation, performance analysis, and resource allocation in CF FD massive multiple-input multiple-output (mMIMO) networks, supported by an extensive literature review and case studies.