We study the spectral properties of magnetic edge states, which exist in the interior
and exterior spectra of magnetic quantum billiards. To quantize the billiards,
the boundary integral method is extended to the magnetic problem and
to general boundary conditions. By virtue of an analytical regularization of the
(hyper-)singular integral operators, we obtain for the first time precise quantum
spectra even in the extreme semiclassical regime. The insight gained into the
structure of the spectral determinant enables us to derive the semiclassical trace
formula for magnetic billiards from first principles. We propose a spectral measure,
which quantifies the intuitive notion of edge states. This density of edge
states allows to analyse the interior and exterior spectra statistically, and to describe
them semiclassically. We find strong, non-trivial cross-correlations between
the interior and exterior spectra. These correlations are based on a duality
of the corresponding classical dynamics. Our analytical results are confirmed by
extensive numerical studies.