Thousands of transiting exoplanets have been discovered to date, thanks in great part to the Kepler space mission. As in all populations, and certainly in the case of exoplanets, one finds unique objects with distinct characteristics. Here we will describe the properties and behaviour of a small group of 'disintegrating' exoplanets discovered over the last few years (KIC 12557548b, K2-22b, and others). They evaporate, lose mass unraveling their naked cores, produce spectacular dusty comet-like tails, and feature highly variable asymmetric transits. Apart from these exoplanets, there is observational evidence for even smaller 'exo-'objects orbiting other stars: exoasteroids and exocomets. Most probably, such objects are also behind the mystery of Boyajian's star. Ongoing and upcoming space missions such as TESS and PLATO will hopefully discover more objects of this kind, and a new era of the exploration of small extrasolar systems bodies will be upon us.