Recent application of carbonate Pb-Pb and U-Pb geochronology has made an important contribution to the dating of primary deposition (strictly speaking, early diagenesis) or metamorphism of sedimentary sequences. The present article summarizes some highlights of this development, discusses the functioning of carbonate U-Pb and Pb-Pb chronometers, and outlines major advantages, drawbacks and some problems to be resolved in the future. Like in all classic dating methods (Rb-Sr, K-Ar, Sm-Nd, U-Pb zircon), the validity of U-Pb and Pb-Pb ages of non-metamorphosed carbonates rests upon the closed-system behavior of U and Pb. Carbonate U-Pb or Pb-Pb ages alone do not yield conclusive geologic meanings. However, for metamorphic carbonates, Pb-Pb isochron ages of marbles generally reflect faithfully the time of metamorphic recrystallisation. Additional information on the thermal histories and U-Pb fractionation of carbonates may be obtained using the three-dimensional approach of Wendt (1984). The available data for carbonates from 16 localities, with ages ranging from Archean to Mesozoic, show that except for one case (Mushandike Limestone) all model mu1-values have a small range of 8.4+/-0.4. Very high mu1-value as would be expected from a closed-system isotopic homogenization in metamorphic carbonates has never been observed, suggesting: (1) in diagenetic or metamorphic conditions, Pb was homogenized in an open system containing both carbonate and extraneous Pb; and (2) the extraneous Pb had a signature of major terrestrial reservoir, which dominated the Pb budget in the renewed carbonate U-Pb isotopic systems. The published U-Pb and Pb-Pb ages so far are not sufficiently precise to be useful in the calibration of geologic time scale for the Phanerozoic. Despite many carbonate rocks have been reasonably dated by the U-Pb and Pb-Pb methods, there are cases of failure (no isochron obtained) and results of ambiguous geological significance (disturbed isotopic systems). Several important problems remain to be answered: (1) modes of carbonate formation and U-Pb incorporation; (2) processes of dolomitization and their relation with U and Pb redistribution; (3) time interval between deposition and diagenesis/dolomitization; (4) Pb isotopic homogenization and U-Pb redistribution during all stages of diagenesis and metamorphism; and (5) identification of uranium carriers in carbonates.