This paper reviews the advancements and challenges in the field of radar-communication spectrum sharing (CRSS), focusing on both radar-communication coexistence (RCC) and dual-functional radar-communication (DFRC) systems. The authors highlight the increasing demand for sharing frequency bands between radar and communication systems, driven by the need to utilize underutilized spectral resources. They discuss various application scenarios, including coexistence of individual radar and wireless systems, 5G mmWave localization for vehicular networks, Wi-Fi-based indoor localization and activity recognition, and unmanned aerial vehicle (UAV) communication and sensing. The paper also reviews recent research progress in CRSS, covering opportunistic spectrum access, interference channel estimation, closed-form precoder design, optimization-based designs, and receiver designs. Additionally, it explores information theory for DFRC, temporal and spectral processing, and spatial processing. The authors propose a novel mmWave mMIMO DFRC architecture that can simultaneously detect targets and communicate with a user equipment (UE) while serving as a base station (BS). They introduce a TDD frame structure that unifies radar and communication operations, and present joint signal processing strategies for target search, communication channel estimation, transmit beamforming, and target tracking. The paper concludes with numerical results and identifies future research directions in the field of CRSS.This paper reviews the advancements and challenges in the field of radar-communication spectrum sharing (CRSS), focusing on both radar-communication coexistence (RCC) and dual-functional radar-communication (DFRC) systems. The authors highlight the increasing demand for sharing frequency bands between radar and communication systems, driven by the need to utilize underutilized spectral resources. They discuss various application scenarios, including coexistence of individual radar and wireless systems, 5G mmWave localization for vehicular networks, Wi-Fi-based indoor localization and activity recognition, and unmanned aerial vehicle (UAV) communication and sensing. The paper also reviews recent research progress in CRSS, covering opportunistic spectrum access, interference channel estimation, closed-form precoder design, optimization-based designs, and receiver designs. Additionally, it explores information theory for DFRC, temporal and spectral processing, and spatial processing. The authors propose a novel mmWave mMIMO DFRC architecture that can simultaneously detect targets and communicate with a user equipment (UE) while serving as a base station (BS). They introduce a TDD frame structure that unifies radar and communication operations, and present joint signal processing strategies for target search, communication channel estimation, transmit beamforming, and target tracking. The paper concludes with numerical results and identifies future research directions in the field of CRSS.