  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.
