  We study sufficient conditions for the absence of positive eigenvalues of
magnetic Schr\"odinger operators in $\mathbb{R}^d,\, d\geq 2$. In our main
result we prove the absence of eigenvalues above certain threshold energy which
depends explicitly on the magnetic and electric field. A comparison with the
examples of Miller--Simon shows that our result is sharp as far as the decay of
the magnetic field is concerned. As applications, we describe several
consequences of the main result for two-dimensional Pauli and Dirac operators,
and two and three dimensional Aharonov--Bohm operators.
