The Terrestrial Planet Finder (TPF) is a space-based astronomical telescope that will combine high sensitivity and spatial resolution to detect and characterize /spl sim/150 planetary systems within 15 pc of our Sun. In a five-year mission, currently expected to commence in 2012, TPF will look for the atmospheric signatures of life using the methods of planetary spectroscopy. This is only possible if implemented within a telescope or interferometer whose spatial resolution is capable of resolving the planet as distinct from its parent star, and yet being able to suppress the starlight to a level of 10/sup -6/ or better. The design of TPF that had been used to illustrate the feasibility of the mission was an interferometer composed of a four-element linear array of 3.5-m diameter telescopes situated in an orbit at L2 and observing over the spectral band of 3-30 /spl mu/m. At these wavelengths an Earth-like planet would be more easily detectable in the glare of the parent star, but the angular resolution required for planet detection implies telescope separations of between 75 and 200 m, and separations of up to 1000 m would be needed for general astrophysics. The interferometer had therefore been envisaged as an array of free-flying telescopes. More recent design studies for TPF have also considered the possibility of having it built as a single-aperture optical telescope. The required angular resolution for planet detection could then be achieved with a mirror spanning 8 or 10 m in diameter. Possible designs include coronagraphs with circular, square, rectangular, or other shaped entry pupils, with tapered transmission across the pupil to suppress unwanted sidelobes in the diffraction pattern. Coronagraphs with phase masks have also been proposed to more efficiently suppress starlight. For these coronagraphs the principal challenges include not only the suppression of scattered light but the design of adaptive optics systems with sub-nm control. The design requirements and the current status of research are reviewed.