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We review the basic kinetic wealth-exchange models of Angle [J. Angle, Social Forces 65, 293 (1986); J. Math. Sociol. 26, 217 (2002)], Bennati [E. Bennati, Rivista Internazionale di Scienze Economiche e Commerciali 35, 735 (1988)], Chakraborti and Chakrabarti [A. Chakraborti, B. K. Chakrabarti, Eur. Phys. J. B 17, 167 (2000)], and of Dragulescu and Yakovenko [A. Dragulescu, V.M. Yakovenko, Eur. Phys. J. B 17, 723 (2000)]. Analytical fitting forms for the equilibrium wealth distributions are proposed. The influence of heterogeneity is investigated, the appearance of the fat tail in the wealth distribution and the relaxation to equilibrium are discussed. A unified reformulation of the models considered is suggested.