The boundaries between physical and social networks have narrowed with the advent of the Internet and its pervasive platforms. This has given rise to a complex adaptive information ecosystem where individuals and machines compete for attention, leading to emergent collective phenomena. The flow of information in this ecosystem is often non-trivial and involves complex user strategies from the forging or strategic amplification of manipulative content to large-scale coordinated behavior that trigger misinformation cascades, echo-chamber reinforcement, and opinion polarization. We argue that statistical physics provides a suitable and necessary framework for analyzing the unfolding of these complex dynamics on socio-technological systems. This review systematically covers the foundational and applied aspects of this framework. The review is structured to first establish the theoretical foundation for analyzing these complex systems, examining both structural models of complex networks and physical models of social dynamics (e.g., epidemic and spin models). We then ground these concepts by describing the modern media ecosystem where these dynamics currently unfold, including a comparative analysis of platforms and the challenge of information disorders. The central sections proceed to apply this framework to two central phenomena: first, by analyzing the collective dynamics of information spreading, with a dedicated focus on the models, the main empirical insights, and the unique traits characterizing misinformation; and second, by reviewing current models of opinion dynamics, spanning discrete, continuous, and coevolutionary approaches. In summary, we review both empirical findings based on massive data analytics and theoretical advances, highlighting the valuable insights obtained from physics-based efforts to investigate these phenomena of high societal impact.