The three chapters presented in the following apply the concept of general equilibrium to topics related to labor markets. The first chapter "Decentralization of wage bargaining" focuses on the changes in collective bargaining institutions that a number of European countries have witnessed in the last decades, with a tendency towards more decentralized wage negotiations, especially in the Scandinavian countries. In particular, this first chapter analyzes the reason why centralized systems of wage bargaining that have performed very well in terms of macroeconomic variables, collapse. We construct a general equilibrium model with matching in the labor market and include a federation of unions, which are coalitions of heterogeneous workers, whose role is to bargain wages for the workers with the firms taking into account redistributive issues, so as to create a framework able to replicate the Scandinavian labor markets for the seventies. We show that the collapse of this system is a consequence of a skill-biased technical change that increases the differences across workers making this kind of coalition unsustainable. The second chapter "An estimated DSGE-matching model for the US economy" estimates via maximum likelihood a DSGE model using US data. The theoretical model is an extended version of the RBC Andolfatto (1996) model of frictional labor markets, in which beyond the standard neutral technology shock we have introduced a preference shock in the utility function, an investment-specific technology shock and a job-separation shock. Once estimated, we perform a variance decomposition analysis to identify which shocks are driving the cyclical fluctuations of the main variables of the model. The results show that the neutral and the investment-specific technology shocks explain most of the fluctuations of the variables of the model; and that the shock to job destruction is successful in explaining the variance of tightness. The third chapter "A RBC model with unemployed loss of skills" proposes a model of frictional labor markets with two types of workers: high-skilled and low-skilled workers, where high-skilled workers may suffer from a depreciation of their human capital while unemployed. We estimate the parameters of the model via maximum likelihood and analyze the its cyclical properties. We also contribute to the literature that tries to explain the different performance of European and US unemployment reconciling the macro and micro evidence.