In this talk we present results related to the convergence of multilevel/multigrid methods, applied to symmetric positive definite linear systems. The presentation is based on the subspace correction framework. The abstract theory is applied to examples coming from finite element discretizations of scalar elliptic partial differential equations and we show how some of the known estimates of the convergence rate of the multigrid method can be obtained in a straightforward fashion. We also discuss some relations between a multiplicative Schwarz method convergence and the condition number of the corresponding additive Schwarz preconditioner.