The pathway of radio astronomy to the SKA ---A focus on the astrophysics of galaxy clusters and on the large-scale structure of the Universe.

Radio astronomy is undergoing a major transformation. Developments in high-speed digital signal processing and broad-band optical fiber links have allowed to realize advanced radio telescopes ($e.g.$, LOFAR, MWA, ASKAP, MeerKAT), precursors and pathfinders for the future Square Kilometer Array (SKA). The unprecedented capabilities of these facilities are currently revolutionizing radio astronomy, yielding frontier science in cosmology and astrophysics. In particular, the pan-European LOFAR array is the world's largest effort to explore the radio sky at long wavelengths. It is a network of stations, distributed across Europe, that produces unprecedented data volumes and opens a new observational window of the Universe. In this contribution I will first provide a brief overview of the most important science questions and areas that are driving the scientific roadmap toward the SKA. In the second part of the contribution I will focus on the astrophysics of non-thermal phenomena in galaxy clusters and large-scale structure of the Universe, discussing the most relevant phenomenological and physical aspects and the enormous progress we are achieving through the exploitation of LOFAR data.