  The spectrum of the Laplace operator in a curved strip of constant width
built along an infinite plane curve, subject to three different types of
boundary conditions (Dirichlet, Neumann and a combination of these ones,
respectively), is investigated. We prove that the essential spectrum as a set
is stable under any curvature of the reference curve which vanishes at infinity
and find various sufficient conditions which guarantee the existence of
geometrically induced discrete spectrum. Furthermore, we derive a lower bound
on the distance between the essential spectrum and the spectral threshold for
locally curved strips. The paper is also intended as an overview of some new
and old results on spectral properties of curved quantum waveguides.
