Extrasolar enigmas: from disintegrating exoplanets to exoasteroids

Thousands of transiting exoplanets have been discovered to date, thanks in great part to the {\em 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 {\em 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.Comment: Accepted for publication in the book "Reviews in Frontiers of Modern Astrophysics: From Space Debris to Cosmology" (eds Kabath, Jones and Skarka; publisher Springer Nature) funded by the European Union Erasmus+ Strategic Partnership grant "Per Aspera Ad Astra Simul" 2017-1-CZ01-KA203-03556