Phase-Induced Amplitude Apodization (PIAA) is a high performance coronagraphic technique well suited for direct imaging and spectroscopic characterization of potentially habitable Earth-like planets from space. It delivers high contrast images by performing a lossless geometric remapping of the telescope beam with two aspheric mirrors, and simultaneously offers nearly full throughput, full angular resolution of the telescope, small inner working angle, high contrast and low chromatism. While the early PIAA systems (which are currently undergoing testing at several facilities) were designed to deliver high contrast at 2 l/D, newer hybrid designs can theoretically deliver on a point source a 1e-10 contrast down to 0.64 l/D inner working angle with full throughput, approaching limits imposed by fundamental principles. PIAA coronagraph designs offer nearly optimal coronagraphic solutions for a wide range of telescope size and astrophysical goals, from debris disks and giant planet imaging with a small size (