Our work uses ground and space-based telescopes to observe debris disks over a wide range of wavelengths. The dust is heated by the star and can be observed by its thermal emission in the mid-IR to sub-mm; this thermal emission is detected either as an excess above the star's photospheric emission or as emission that is extended from the otherwise point-like star. In some cases starlight scattered off the dust can be imaged at optical wavelengths. We use (or have used) telescopes/instruments such as: HST, SPHERE, VISIR, MIDI, WISE, Spitzer, Herschel, JCMT, and ALMA.
We have recently completed an unbiased survey of a sample that covers the nearest ~500 stars (or rather the nearest ~100 of each spectral type A,F,G,K,M). The DEBRIS survey used the Herschel satellite to search for far-IR emission from dust, detecting it around roughly 20 percent of other stars like our Sun. The figure below shows a resolved image of the 150au radius debris disk around eta Crv (Duchene et al 2014), observed at a wavelength of 70 microns. Our group has also characterised a second dust population much closer to this star (Smith et al 2009), and the popular interpretation is that this system is undergoing an event similar to the Late Heavy Bombardment.
We also perform follow-up observations to characterise known debris disks. For example, the figure below shows two images of the disk around beta Pictoris. The upper image shows dust emission from the edge on disk, and that the dust is clumped such that it is brighter on the West (right) side of the star than on the East. The lower image shows emission from CO gas, which is clumped in a similar, but even more extreme manner. The conclusion from these observations (Dent et al 2014) is that the CO is probably released during the same destructive cometary collisions that generate the dust. The fate of this gas, and of atomic species such as C and O, is one aspect of our theoretical work.