Cluster radioactivity (spontaneous emission of heavy particles from nuclei) is presented from theoretical point of view in good agreement with experimental results. After a brief hystorical account we give details about the analytical super asymmetric fission (ASAF) model extensively used for predicting the half-lives of heavy and superheavy (Z ≥ 104) elements. For the already measured 26 cluster decays (from 14C to 32,34Si of parent nuclides with Z = 87-96) it is clear that cluster radioactivity is a rare phenomenon in the best case about 9 orders of magnitude weaker than the competing alpha decay. Then we show the theoretical possibility of a strong cluster decay compared to alpha decay for some superheavy nuclei with Z ≥ 122, e.g. 306122; 310-314122; 306-324124, and 311-323124.