In this talk I will discuss numerical results how surface disorder affects the transport in topological insulators and their close cousins Weyl semimetals that are known for their disorder tolerant surface states. Charge and spin currents will be calculated and their dependence on surface disorder will be studied for a model of 3D topological insulator. Here we will show a new aspect of spin generation where the role of the insulating yet topologically non-trivial bulk becomes explicit: an external electric field creates a transverse pure spin current through the bulk of a 3D TI, which transports spins between the top and bottom surfaces and leads to spin accumulation on both. This new spin generation mechanism results in a distinct strategy for the enhancement of surface spin polarization by increasing nonmagnetic impurity concentration. Next, studies of a Weyl semimetal model will be discussed and contrasted to the case of topological insulator. In particular, I will discuss scattering as a function of the shape of the Fermi arc where we find that the impact on surface transport is significantly dependent on the arc curvature. We find that the limit of a straight arc geometry is remarkably disorder tolerant, producing surface conductivity that is one to two orders of magnitude larger of a comparable set up with surface states of TI. Finally, a simulation of the effects of surface vacancies on TaAs will be presented, illustrating the disorder tolerance of the topological surface states in a recently discovered WSM material.