Since the time Roberts & Scott (1965) first expressed the key 'frozen flux' hypothesis relating the secular variation of the geomagnetic field (SV) to the flow at the core surface, a large number of studies have been devoted to building maps of the flow and inferring its fundamental properties from magnetic observations at the Earth's surface. There are some well-known difficulties in carrying out these studies, such as the one linked to the non-uniqueness of the flow solution [if no additional constraint is imposed on the flow (Backus 1968)] which has been thoroughly investigated. In contrast little investigation has been made up to now to estimate the exact importance of other difficulties, although the different authors are usually well aware of their existence. In this paper we intend to make as systematic as possible a study of the limitations linked to the use of truncated spherical harmonic expansions in the computation of the flow. Our approach does not rely on other assumptions than the frozen flux, the insulating mantle and the large-scale flow assumptions along with some simple statistical assumptions concerning the flow and the Main Field. Our conclusions therefore apply to any (toroidal, steady or tangentially geostrophic) of the flow models that have already been produced; they can be summarized in the following way: first, because of the unavoidable truncation of the spherical harmonic expansion of the Main Field to degree 13, no information will ever be derived for the components of the flow with degree larger than 12; second, one may truncate the spherical harmonic expansion of the flow to degree 12 with only a small impact on the first degrees of the flow. Third, with the data available at the present day, the components of the flow with degree less than 5 are fairly well known whereas those with degree greater than 8 are absolutely unconstrained.