Shortcomings of the representation of the topside electron density profile in the International Reference Ionosphere (IRI) model have been noted in comparison with recently analyzed topside sounder data and also with total electron content (TEC) data. Various studies have proposed corrections of the IRI formulas or have introduced a new formalism. This paper reviews the different approaches, their implications for IRI, and their current status. An important challenge for topside modeling is the truthful representation of profiles in the equatorial anomaly (EA) region over the whole range of the EA fountain. This means that the latitudinal representation has to reproduce the merging of the double-peak signature at F region heights into a single peak at the top of the fountain. In this context, special emphasis is given to the coupling between topside and plasmaspheric models.