The name perovskite has been dated back to 1839 when Rose, a Russian mineralogist, discovered a new mineral CaTiO3, which he baptized perovskite after the then Russian Minister of Lands, count L.A.Perovsky. This name has been later used to designate a large ABO3 perovskite family. A lot of well-known classical ferroelectrics belong to this family. Two members of the family, SrTiO3 and KTaO3, have a polar soft mode, but do not exhibit a ferroelectric phase transition similar to 4He quantum liquid in which a crystalline state has never been realized at normal pressure. This is explained by the stabilization of their paraelectric phase by quantum fluctuations [1,2]. So SrTiO3 and KTaO3 are quantum paraelectrics or incipient ferroelectrics. They may be, in a certain sense, classified as marginal systems which are at the limit of their paraelectric phase stability. Small perturbations can destroy the stability and induce a ferroelectric phase. For example, SrTiO3 becomes a ferroelectric at low temperatures under action of an uniaxial stress of only 1 kbar [3,4] or under application of a static electric fields as low as 1 kV/cm [5, 6, 7]. This means that elastic lattice strains about 104 and electric fields of the order of 10-5 of atomic fields are sufficient to induce a ferroelectric phase. It appeares [8,9] that impurities with concentration around 10-3 can also destroy the stability of the paraelectric phase and induce a ferroelectric phase. Just the effect of various impurities on phase transitions in the incipient ferroelectrics will be discussed in the present paper. The main attention will be paid to SrTiO3 but KTaO3 and a new incipient ferroelectric CaTiO3 will be also shortly discussed.