The systems that arise fluid mechanics are inevitably too complex to meet expediency
requirements of stability analysis, optimization and control. In this talk, the
increasingly popular matrix-free methods, that have been devised so that complex flows
are amenable to analysis, are outlined. The techniques share a common methodology: very
large eigenvalue problems are solved based only on snapshots of fields at different
points in time. No large matrices are stored. Therefore the main tool is a numerical code
that time integrates the forward and adjoint governing equations.