The interaction of ultrafast laser pulses of relativistic intensity with high aspect ratio nanostructures can efficiently and volumetrically heat matter to an ultra-high-energy-density regime encountered in the center of stars and within the core of fusion capsules compressed by the world’s largest lasers. It also generates gigantic quasi-static electromagnetic fields that accelerate particles to very high energy. Here, we present an overview of the physics and applications of these dense relativistic plasmas that can be created with pulses of relatively modest energy from lasers that can operate at a high repetition rate. Recent nanowire array experiments produced near-solid density plasmas with an extreme degree of ionization (e.g., Au+72), converted ultrafast pulses of laser light into intense x-ray flashes with record efficiency, and accelerated ions to MeV energies, efficiently driving micro-scale fusion reactions that generate flashes of quasi-monoenergetic neutrons. These plasmas also serve as a platform for advancing the understanding of atomic processes in extreme environments and open a new pathway to laser-driven fusion energy. The irradiation of nanostructures at intensities of >1×1022Wcm−2 is predicted to lead to an extreme ultra-high energy density plasma regime characterized by terabar pressures that is virtually unexplored.