This master thesis deals with two types of convergence in economics - beta and sigma convergence. Beta convergence is defined as the negative relationship between the income growth and the initial income level, whereas sigma convergence takes place, if the dispersion of income falls over time. The region analysed is the European Union, a supranational organization with specific, long-lasting regional policies. The empirical analysis answers two questions whether beta and sigma convergence hypotheses apply in EU28 and whether the recent Global Financial Crisis affected the convergence process, if existent, in EU28. The methodology includes four estimators for beta convergence. These are population-weighted and unweighted standard deviation of the logarithm per capita GDP, the coefficient of variation of the logarithm per capita GDP and Kernel densitites. There are five models on -convergence applied for the -convergence research. These are three cross-sectional approaches, based on the methdologies applied by Baumol (1986), Romer, Mankiw and Weil (1992), Barro and Sala-i-Martin (1992), one dynamic panel data model and one time-series model. The results on both beta and sigma convergence are mixed and not stable over time or across the two subgroups, EU15 and the new MS. The results show sigma divergence in the years 1990-1999 for EU28 and 2008-2014 for EU15. The period 2000-2008 confirms sigma convergence for EU28. The results on beta convergence confirm absolute beta convergence during the period 1990-2014, after testing dynamic panel data models. Time-series analysis confirms convergence for 9 out of 28 member states. Further analysis on regional data could provide more insights on developments within the countries in the EU.