The thin flux tube approximation cannot describe some important phenomena occurring during the journey of the tubes across the convection zone. This review summarizes five of those processes. One of them is related to the dramatic off-axis expansion suffered by the top of some magnetic tubes of moderate field strength in the middle of the convection zone. Another one concerns the expansion that all rising tubes experience in the final few 10000 km below the photosphere. The thin flux tube approximation does not account for the development of vorticity and twist in the magnetic tubes (or only under very restrictive circumstances). However, vorticity and twist are fundamental ingredients that have to be considered at various stages of the rise. All this is explained on the basis of the recent results of two-dimensional MHD simulations of the initial stages of the rise. In the final section, the validity of the local approach for a rectilinear and non-rotating tube as well as its failure in more general cases are explained.