Abstract: Reylaigh-Benard convection in binary fluid mixtures withthrough-flow provides a particular of useful model for the study of patternformation and nonlinear dissipative waves in open flow systems. In thispaper we will introduce some preliminary research results for thissystem. First, wepresent briefly the linear stability analysis and discuss the influence ofthrough-flow on the nonlinear bifurcation of spatial uniform patterns. Then,we focus on our results about the traveling-wave convection of this systemin limited spaces with non-periodic boundary conditions, including existingspatiotemporal states and the dependence of their properties on Rayleighnumber and the aspect rations of the channel. Instead, somefurther studies for this system are outlined.