  This paper reviews the most popular methods which are used in lattice QCD to
compute the determinant of the lattice Dirac operator: Gaussian integral
representation and noisy methods. Both of them lead naturally to matrix
function problems. We review the most recent development in Krylov subspace
evaluation of matrix functions. The second part of the paper reviews the formal
relationship and algebraic structure of domain wall and overlap fermions. We
review the multigrid algorithm to invert the overlap operator. It is described
here as a preconditioned Jacobi iteration where the preconditioner is the Schur
complement of a certain block of the truncated overlap matrix.
