Zintl phases have led to many high performance thermoelectric materials. Ab initio computations are a powerful tool to understand electrical and thermal transport in these complex materials. In this talk, I will focus on two antimonides systems: the M3X2 (M=Mg, Ca, X=Sb, Bi…) and A14MX11 (A=Yb, Ca M=Mn, Mg, X=Sb, Bi…) showing promising thermoelectric properties. Using ab initio computations, I will show how surprising experimental findings (e.g., dependence of transport data on atomic substitutions or on temperature) can be explained combining ab initio and experimental results. I will finish my talk by showing how ab initio computations can not only be used to understand but also predict new thermoelectric materials by performing high-throughput screening computations.