Short answer is the resistivity increases until it transitions to insulator.
A band description makes things more clear. Before the transition, the electronic states are pertubatively connected to to disorderless band conductor. After the transition to an insulator the electronic states all become localized and in momentum space this shows up as a band gap around the fermi energy and effectively looks like a band insulator. This is anderson localization: https://en.wikipedia.org/wiki/Anderson_localization
Long answer: Its complicated and not fully understood. In 1D there is no transition. The smallest amount of disorder will localize the system. But at a certain interaction strength the system will delocalize and start conducting again.
Out side of 1D, the non interacting case can be described with different effect models, where usually another or multiple effective fields are introduced which interact with the electron field to cause localization. Here the normal mean field description of a phase transition works and can give you universal scaling relations at the transition. For some discussion you can see this review for the super symmetric method: http://arxiv-export-lb.library.cornell.edu/abs/1002.2632
But things are more complicated and there might not be a simple transition. The griffiths effect describes the possibility of rare regions to localize or delocalize the system in the traditionally conducting or insulating limits. This then creates a middle zone between the transition from conductor to insulator where rare regions play a more important role and may smooth the transition to a cross over.
Finally there has been observations that disorder can actually delocalize a mott insulator(where a gap opens around the fermi surface due to interactions). Here disorder increases conductivity: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.206402