  This is a survey of recent results on zeta- and eta-function poles and values
for realizations of Laplace- and Dirac-type operators defined by
pseudodifferential projection boundary conditions (including the
Atiyah-Patodi-Singer operator and its square). Section 1 recalls some useful
results for ps.d.o.s on closed manifolds. Section 2 describes the asymptotic
trace expansions for second-order operators under general projection boundary
conditions, in particular the vanishing of the zeta residue at 0 in general
(with consequences for first-order operators). Section 3 treats cases with
symmetry or selfadjointness conditions, where a stability of the zeta value at
0, or of the vanishing of the eta residue, can be shown for low-order
perturbations of the boundary projection. Section 4 describes general results
on stability of expansion coefficients when the interior operator is perturbed,
and ends with special results obtainable when the perturbation commutes with
the interior operator near the boundary, in a suitable sense.
