Nanostructured mixtures of ionic liquids and polymers are of great interest for a wide variety of electrochemical applications. Understanding the relationship between composition, structure, and ionic conductivity for these mixtures is essential for designing new materials. In this work, the effect of nanostructure on ionic conductivity, sigma, is investigated for model mixtures of diblock copolymers and ionic liquids that strated that the concentration dependence of sigma is a function of the total volume fraction of ionic liquid and described well by percolation theory. This scaling behavior encourages the design of membranes where the amount of a mechanical component in the block copolymer can be increased to improve the strength of the membrane without sacrificing conductivity. The temperature dependence of sigma is a function of the amount of ionic liquid exclusively in the conducting domain. Comparing sigma for mixtures of the diblock copolymer poly(styrene-block-2-vinylpyridine) (S2VP) and two different ionic liquids, imidazolium bis(trifluoromethylsulfonyl)imide ([Im][TFSI]) and 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([EMIm][TFSI]), reveals that the chemistry of the polymer/ionic liquid pair affects both the activation energy for sigma and the maximum attainable sigma but does not affect how sigma scales with ionic liquid concentration. The effect of the morphology on sigma is also examined, and it is found that as long as the conducting phase morphology is isotropic and well-connected, sigma is not affected by morphology.