Holography is a tool that can be most readily applied to studies of transport properties in gauge theories with infinitely strong interactions. Coupling constant corrections can then be incorporated through higher-derivative (alpha-prime) corrections to the supergravity action in the bulk. In the first part of this talk, I will discuss the dependence of higher-order hydrodynamic transport (beyond Navier-Stokes) and the higher-frequency (quasi-normal) spectrum on the coupling constant in duals of Type IIB supergravity and curvature-squared theories. In relation to the membrane paradigm, I will then present higher-order generalisations of the universal "eta over s" relation and universal anomalous conductivities at finite coupling. Recently, studies of holographic transport in the presence of broken translational symmetry and disorder have received much attention. In particular, it has been shown how thermo-electric conductivities can be computed by using the membrane paradigm. Through the power of the membrane paradigm and with a view towards future models of many-body localisation without hydrodynamic transport, in the second part of this talk, I will discuss the proofs of the lower bounds on thermal and electrical conductivities in a large family of holographic theories with arbitrarily strong disorder.