I will present some recent results on the secular evolution of Milky Way-type galaxies, focusing on the effects of bars and boxy/peanut bulges on the redistribution of gas and stars. Using orbital structure analysis and hydrodynamic gas response simulations I will show how boxy/peanut bulges reduce the bar-induced gas inflow to the nuclear regions of galaxies. I will then present results from N-body simulations of isolated disc galaxies with both a thin and a thick stellar disc which evolve secularly. I will show how these two populations are mapped into a boxy/peanut bulge by the bar, how the weight of the two populations changes along the b/p structure and the resulting morphological, kinematic and chemical characteristics. I will discuss these results in light of the properties of the Milky Way bulge, and of the chemo-kinematic relations satisfied by its main stellar populations.