An object in rotation will in general produce brightness variations that can be measured giving rise to what we call lightcurves. Such lightcurves are produced by various mechanisms: i) albedo variations on the body surface, ii) non-spherical shape, and/or iii) contact or eclipsing binary.
The rotational properties of asteroids provide information about important physical properties, such as shape, density, cohesion etc. As for asteroids, the rotational properties of the Trans-Neptunian Objects and Centaurs provide a wealth of knowledge about the basic physical properties of these icy bodies. In addition, rotational properties provide valuable clues about the primordial distribution of angular momentum, as well as the degree of collisional evolution of the different dynamical groups in the Trans-Neptunian belt.
Less than 10 years ago, only ~50 objects with short-term variability were reported and many published rotational periods were uncertain or erroneous. Increasing the sample size, improving rotational periods, lightcurves, and trying to overcome some observational biases were some of the objectives of my PhD. I have observed most of the brightest known Trans-Neptunian Objects and Centaurs, and have compiled one of the largest samples of lightcurves trying to avoid some observational biases ([.pdf], [.pdf]). Unfortunately, less than 6% of the known Trans-Neptunian Objects have a well-determined rotational period, and the sample of studied objects is highly biased towards objects with large lightcurve amplitudes, short rotational periods, and principally towards bright objects.