We review the recent progress in the exploration of the interrelations between primitive small bodies of the solar system which are preserved the pristine material in their interior: cometary nuclei, Transneptunian Objects, Centaurs, and primitive asteroids, and they are considered as primordial objects. In addition, we discuss the properties of the asteroid-comet transition objects which have really enigmatic behavior. The comets have most primitive, accessible material in the solar system but we do not know what is hidden below the evolved surface layers. Comets must become dormant but we do not know whether the ice is exhausted or sublimation is inhibited (blocked by quenching mechanisms). There must be many dormant comets masquerading as asteroids but we do not know to identify these bodies unless via serendipitous discovery observations. Indeed, there are some asteroids which temporarily show comet-like activity. These are among the Damocloids (C/2001 OG108 (LONEOS)), main belt asteroids (7968 Elst-Pizarro = 133P/E-P) and Near-Earth objects (4015 Wilson-Harrington = 107P/W-H). The important questions are: where is the pristine material in the cometary nuclei and in the asteroid-comet transition objects, do comets lose their ice or seal it in? Both the large survey projects and in-situ space missions will help to answer these questions in the near future.