  Understanding the metal-insulator transition in disordered many-fermion
systems, both with and without interactions, is one of the most challenging and
consequential problems in condensed matter physics. In this paper we address
this issue from the perspective of the modern theory of the insulating state
(MTIS), which has already proven to be effective for band and Mott insulators
in clean systems. First we consider noninteracting systems with different types
of aperiodic external potentials: uncorrelated disorder (one-dimensional
Anderson model), deterministic disorder (Aubry-Andr\'e Hamiltonian and its
modification including next-nearest neighbour hopping), and disorder with
long-range correlations (self-affine potential). We show how the many-body
localisation tensor defined within the MTIS may be used as a powerful probe to
discriminate the insulating and the metallic phases, and to locate the
transition point. Then we investigate the effect of weak repulsive interactions
in the Aubry-Andr\'{e} Hamiltonian, a model which describes a recent cold-atoms
experiment. By treating the weak interactions within a mean-field approximation
we obtain a linear shift of the transition point towards stronger disorder,
providing evidence for delocalisation induced by interactions.
