Nuclear cosmochronometry is a direct method to measure cosmic age. It has been believed that the abundance ratio of Th/Eu is a reliable chronometer and Th/Eu ratios of metal-poor stars have been studied intensively to obtain a lower limit of Galactic age. However, after the actinide-boosted metal-poor star CS 31082-001 had been found, applicability of Th/Eu chronometer to metal-poor stars became questionable. Furthermore, theoretical r-process calculations indicate that the Th/Eu production ratios strongly depend on the nucleosynthesis environment compared to other stable elements between the second and third peak, including Pb. It is impossible to determine the Th/Eu production ratio by theoretical study at this point, though it is essential for the chronometer. Besides, observed universality of r-process abundances does not guarantee a universal Th/Eu production ratio anymore. Th/Eu chronometer is now facing a serious crisis. On the other hand, the U/Th production ratio obtained by theoretical calculation does not depend on the nucleosynthesis environment significantly. Although there is only one U measurement of metal-poor stars at this point, the U/Th chronometer seems to be still robust. Many uncertainties related to data analyses and nuclear physics models still remain to be resolved.