  In this paper,under an abstract setting we establish the existence of
spatially inhomogeneous steady states and the asymptotic propagation properties
for a large class of monotone evolution systems without spatial translation
invariance. Then we apply the developed theory to study traveling waves and
spatio-temporal propagation patterns for time-delayed nonlocal equations,
reaction-diffusion equations in a cylinder, and asymptotically homogeneous
KPP-type equations. We also obtain the existence of steady state solutions and
asymptotic spreading properties of solutions for a time-delayed
reaction-diffusion equation subject to the Dirichlet boundary condition.
