There are several ways planets can survive the giant phase of the host star, hence one can consider the case of Earth-like planets orbiting white dwarfs. As a white dwarf cools from 6000 K to 4000 K, a planet orbiting at 0.01 AU from the star would remain in the continuous habitable zone (CHZ) for about 8 Gyr. Polarisation due to a terrestrial planet in the CHZ of a cool white dwarf (CWD) is 102 (104) times larger than it would be in the habitable zone of a typical M-dwarf (Sun-like star). Polarimetry is thus a powerful tool to detect close-in planets around white dwarfs. Multi-band polarimetry would also allow one to reveal the presence of a planet atmosphere, even providing a first characterisation. 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. Preliminary habitability study show also that photosynthetic processes can be sustained on Earth-like planets orbiting CWDs and that the DNA-weighted UV radiation dose for an Earth-like planet in the CHZ is less than the maxima encountered on Earth, hence white dwarfs are compatible with the persistence of complex life from the perspective of UV irradiation.