This paper addresses the topic of integrated sensing and communications (ISAC) in 5G and emerging 6G wireless networks. ISAC systems operate within shared, congested or even contested spectrum, aiming to deliver high performance in both wireless communications and radio frequency (RF) sensing. The expected benefits include more efficient utilization of spectrum, power, hardware (HW) and antenna resources. Focusing on multicarrier (MC) systems, which represent the most widely used communication waveforms, it explores the co-design and optimization of waveforms alongside multiantenna transceiver signal processing for communications and both monostatic and bistatic sensing applications of ISAC. Moreover, techniques of high practical relevance for overcoming and even harnessing challenges posed by non-idealities in actual transceiver implementations are considered. To operate in highly dynamic radio environments and target scenarios, both model-based structured optimization and learning-based methodologies for ISAC systems are covered, assessing their adaptability and learning capabilities under real-world conditions. The paper presents trade-offs in communication-centric and radar-sensing-centric approaches, aiming for an optimized balance in densely used spectrum.