How do wages and labor market transitions vary with labor market concentration?  Using comprehensive French employer-employee data, I show that wages increase – contrary to what has been shown in other countries – and transition rates decrease when concentration increases.  These results are found in the raw data, in regressions at the labor market level, in panel data regressions and in an event study setting in which I focus on markets undergoing large increase in concentration.  I then propose a simple model of search-and-matching with a discrete number of firms, optimal vacancy posting and a fixed cost of entry.  My model replicates my main two empirical findings: (1) when the entry cost increases, only the most productive firms enter, the market is more concentrated, wages are higher, and transition rates are lower; (2) given a labor market, an increase in productivity at one large firm increases wages at all firms through the increase in output at that firm and in outside option at all other firms, increases transition rates towards that firm, and reduces them towards all other firms.  I quantify the markdowns on wages and show they are always relatively small.  I investigate the first-best solution in which a planner chooses the distribution of workers across firms to maximize output: the planner concentrates employment among most productive firms, it increases output, mean wage, and total income to workers despite increasing concentration and unemployment.  I turn to second-best implementations using individual tax and subsidy rates.  By fully taxing most firms - the unproductive ones -, taxing partially the least productive firms among the operating ones, and using the tax revenue collected to subsidize the most productive firms, a planner almost achieves the first-best solution.  On the contrary, simple linear tax policies do no come anywhere close to the first-best solution.