Since there are several ways planets can survive the giant phase of the host star, we examine the habitability and detection of planets orbiting white dwarfs. As a white dwarf cools from 6000 K to 4000 K, a planet orbiting at 0.01 AU would remain in the continuous habitable zone (CHZ) for similar to 8 Gyr. We show that photosynthetic processes can be sustained on such planets. The DNA-weighted UV radiation dose for an Earth-like planet in the CHZ is less than the maxima encountered on Earth, and hence non-magnetic white dwarfs are compatible with the persistence of complex life. Polarization due to a terrestrial planet in the CHZ of a cool white dwarf (CWD) is 10(2) (10(4)) times larger than it would be in the habitable zone of a typical M-dwarf (Sun-like star). Polarimetry is thus a viable way to detect close-in rocky planets around white dwarfs. Multi-band polarimetry would also allow us to reveal the presence of a planet atmosphere, providing a first characterization. Planets in the CHZ of a 0.6 M-circle dot white dwarf will be distorted by Roche geometry, and a Kepler-11d analog would overfill its Roche lobe. With current facilities a super-Earth-sized atmosphereless planet is detectable with polarimetry around the brightest known CWD. Planned future facilities render smaller planets detectable, in particular by increasing the instrumental sensitivity in the blue.