  This paper is devoted to the investigation of spatial spreading speeds and
traveling wave solutions of monostable evolution equations with nonlocal
dispersal in time and space periodic habitats. It has been shown in an earlier
work by the first two authors of the current paper that such an equation has a
unique time and space periodic positive stable solution $u^*(t,x)$. In this
paper, we show that such an equation has a spatial spreading speed $c^*(\xi)$
in the direction of any given unit vector $\xi$. A variational characterization
of $c^*(\xi)$ is given. Under the assumption that the nonlocal dispersal
operator associated to the linearization of the monostable equation at the
trivial solution $0$ has a principal eigenvalue, we also show that the
monostable equation has a continuous periodic traveling wave solution
connecting $u^*(\cdot,\cdot)$ and $0$ propagating in any given direction of
$\xi$ with speed $c>c^*(\xi)$.
