This thesis contributes to the understanding of how socio-economic factors affect the functioning of modern labour markets. It belongs to the strand of academic literature that departs from the standard Walrasian model of the labour market, and considers matching and information frictions to be important determinants of observed labour market phenomena. Within this general framework, this thesis analyses how different forms of agent heterogeneity / socio-demographic identity, productivity, and wealth - affect wage rates and the level of employment in competitive labour markets. The first chapter studies how occupational segregation - the sorting of workers across occupations based on their demographic characteristics - affects the allocation of talent in the labour market. When job vacancy information is transmitted via workers' group-biased social contacts, occupational segregation is found to be a robust equilibrium outcome. The chapter shows that while occupational segregation implies benefits in terms of the job-finding probability of individual workers, it may also engender significant allocative inefficiencies when workers differ in terms of their productivity across occupations. The second chapter examines how heterogeneous workers and firms sort across formal (market-based) and informal (network-based) recruitment channels. When worker and firm productivity are unobservable the two recruitment channels effectively compete in terms of their screening capability. Matching frictions are shown to generate a sorting externality that leads to a multiplicity of equilibrium outcomes, depending on the skill-bias within social networks and the productivity dispersion among workers and firms. The third chapter, co-authored with Damien Puy, examines to what extent variations in wages and employment over the business-cycle can explain the counter-cyclical properties of the income distribution. We show that demand composition effects are an important channel through which aggregate supply shocks are propagated through the economy, and that these have important distributional consequences. In particular, we find income inequality (as measured by the Gini coefficient) to be counter-cyclical. Consistent with empirical evidence, this is shown to be largely due to changes in the level of employment and to a lesser degree to variations in relative factor prices.