A renormalization group method in real space is applied to the study of transport properties of random media. In particular, the method is applied to the study of the electrical properties of disordered materials and the study of the elastic properties of random materials. The theoretical predictions for the conductivity of disordered materials are in excellent agreement with both computer simulations and experimental results. Two microscopic models of elasticity of random materials are studied, the bond-bending model and the central-force model. The critical behavior of the elastic moduli of the bond-bending model is in good agreement with experimental and computer simulation results. The rigidity threshold of the central-force model is found not to correspond to that of pure percolation, and the predicted critical behavior of this model is found to differ markedly from that of the bond-bending model. A method to probe the universality of these two models by studying renormalization group flow diagrams, and an extension of the present method to the study of electrical breakdown and mechanical failure are proposed.