The possibility or even necessity of revising definitions of some of the base units of the present SI has been discussed over the past 15 years. The last General Conference of Weights and Measures (2007) recommended to redefine the kilogram, the ampere, the kelvin, and the mole using fixed values of the fundamental constants by the time of the next General Conference in 2011. This paper is a review of proposals of new definitions of units of mentioned quantities and arguments voting for particular variants of definitions. Most relevant papers for this review have been published by Metrologia, the international journal appointed at the BIPM, and many other useful pieces of information are available on www pages of the BIPM. The author notes that not only new definitions have been discussed but as well as the set of the base units of the SI. It means a replacement of the ampere by the volt or the kelvin by the joule. Decisions concerning new definitions are not made and the discussions are still open.