The correlation coefficient between stocks depends on price history and includes information on hierarchical structure in financial markets. It is useful for portfolio selection and estimation of risk. I introduce the Life Time of Correlation between stocks prices to know how far we should investigate the price history to obtain the optimal durability of correlation. I carry out my research on emerging (Poland) and established markets (in the USA, Great Britain and Germany). Other methods, including the Minimum Spanning Trees, tree half-life, decomposition of correlations and the Epps effect are also discussed.