The fifth generation (5G) cellular network has been commercialized recently to fulfill the new demands such as very high data exchange rate, extra low latency and high reliability. Many new technologies have been introduced and exploited since the early of the 2010s. Among these emerging technologies, full-duplex relaying cognitive radio networks, device-to-device communications and cell-free massive multiple-input and multiple-output have been considered as promising technologies/systems for 5G and beyond. This work provides a comprehensive study on the concepts, advantages and challenges of the above-mentioned technologies. In addition, we also introduce four new research directions which are challenges of 5G and beyond.