Over the last few decades, wireless networks have morphed from traditional cellular/wireless local area networks (WLAN), into a wide range of applications, such as the Internet-of-Things (IoT), vehicular-to-everything (V2X), and smart grid communication networks. This transition has been facilitated by research and development efforts in academia and industry, which has resulted in the standardization of fifth-generation (5G) wireless networks. To meet the performance requirements of these diverse use-cases, 5G networks demand higher performance in terms of data rate, latency, security, and reliability, etc. At the physical layer, these performance enhancements are achieved by (a) optimizing spectrum utilization shared amongst multiple technologies (termed as spectrum sharing), and (b) leveraging advanced spatial signal processing techniques using large antenna arrays (termed as massive MIMO). In this dissertation, we focus on enhancing the performance of next-generation vehicular communication and spectrum sharing systems. In the first contribution, we present a novel pilot configuration design and adaptation mechanism for cellular vehicular-to-everything (C-V2X) networks. Drawing inspiration from 4G and 5G standards, the proposed approach is based on limited feedback of indices from a codebook comprised of quantized channel statistics information. We demonstrate significant rate improvements using our proposed approach in terrestrial and air-to-ground (A2G) vehicular channels. In the second contribution, we demonstrate the occurrence of cellular link adaptation failure due to channel state information (CSI) contamination, because of coexisting pulsed radar signals that act as non-pilot interference. To mitigate this problem, we propose a low-complexity semi-blind SINR estimation scheme that is robust and accurate in a wide range of interference and noise conditions. We also propose a novel dual CSI feedback mechanism for cellular systems and demonstrate significant improvements in throughput, block error rate, and latency, when sharing spectrum with a pulsed radar. In the third contribution, we develop fundamental insights on underlay radar-massive MIMO spectrum sharing, using mathematical tools from stochastic geometry. We consider a multi-antenna radar system, sharing spectrum with a network of massive MIMO base stations distributed as a homogeneous Poisson Point Process (PPP) outside a circular exclusion zone centered around the radar. We propose a tractable analytical framework, and characterize the impact of worst-case downlink cellular interference on radar performance, as a function of key system parameters. The analytical formulation enables network designers to systematically isolate and evaluate the impact of each parameter on the worst-case radar performance and complements industry-standard simulation methodologies by establishing a baseline performance for each set of system parameters, for current and future radar-cellular spectrum sharing deployments. Finally, we highlight directions for future work to advance the research presented in this dissertation and discuss its broader impacts across the wireless industry, and policy-making. / Doctor of Philosophy / The impact of today's technologies has been magnified by wireless networks, due to the standardization and deployment of fifth-generation (5G) cellular networks. 5G promises faster data speeds, lower latency and higher user security, among other desirable features. This has made it capable of meeting the performance requirements of key infrastructure such as smart grid and mission-critical networks, and novel consumer applications such as smart home appliances, smart vehicles, and augmented/virtual reality. In part, these capabilities have been achieved by (a) better spectrum utilization among various wireless technologies (called spectrum sharing), and (b) serving multiple users on the same resource using large multi-antenna systems (called massive MIMO). In this dissertation, we make three contributions that enhance the performance of vehicular communications and spectrum sharing systems. In the first contribution, we present a novel scheme wherein a vehicular communication link adapts to the channel conditions by controlling the resource overhead in real-time, to improve spectral utilization of data resources. The proposed scheme enhances those of current 4G and 5G networks, which are based on limited feedback of quantized channel statistics, fed back from the receiver to the transmitter. In the second contribution, we show that conventional link adaptation methods fail when 4G/5G networks share spectrum with pulsed radars. To mitigate this problem, we develop a comprehensive signal processing framework, consisting of a hybrid SINR estimation method that is robust and accurate in a wide range of interference and noise conditions. Concurrently, we also propose a scheme to pass additional information that captures the channel conditions in the presence of radar interference, and analyze its performance in detail. In the third contribution, we focus on characterizing the impact of 5G cellular interference on a radar system in shared spectrum, using mathematical tools from stochastic geometry. We model the worst-case interference scenario, and study the impact of the system parameters on the worst-case radar performance. In summary, this dissertation advances the state-of-the-art in vehicular communications and spectrum sharing, through (a) novel contributions in protocol design and (b) development of mathematical tools for performance characterization.