  We study Neumann type boundary value problems for nonlocal equations related
to L\'evy processes. Since these equations are nonlocal, Neumann type problems
can be obtained in many ways, depending on the kind of reflection we impose on
the outside jumps. To focus on the new phenomenas and ideas, we consider
different models of reflection and rather general non-symmetric L\'evy
measures, but only simple linear equations in half-space domains. We derive the
Neumann/reflection problems through a truncation procedure on the L\'evy
measure, and then we develop a viscosity solution theory which includes
comparison, existence, and some regularity results. For problems involving
fractional Laplacian type operators like e.g.$(-\Delta)^{\alpha/2}$, we prove
that solutions of all our nonlocal Neumann problems converge as alpha goes to 2
to the solution of a classical Neumann problem. The reflection models we
consider include cases where the underlying L\'evy processes are reflected,
projected, and/or censored upon exiting the domain.
