Casein micelle dispersions have been concentrated through osmotic stress and examined through rheological experiments. In conditions where the casein micelles are separated from each other, i.e., below random-close packing, the dispersions have exactly the flow and dynamic properties of the polydisperse hard-sphere fluid, demonstrating that the micelles interact only through excluded volume effects in this regime. These interactions cause the viscosity and the elastic modulus to increase by three orders of magnitude approaching the concentration of random-close packing estimated at C(max) approximately 178 g/l. Above C(max), the dispersions progressively turn into "gels" (i.e., soft solids) as C increases, with elastic moduli G(') that are nearly frequency independent. In this second regime, the micelles deform and/or deswell as C increases, and the resistance to deformation results from the formation of bonds between micelles combined with the intrinsic mechanical resistance of the micelles. The variation in G(') with C is then very similar to that observed with concentrated emulsions where the resistance to deformation originates from a set of membranes that separate the droplets. As in the case of emulsions, the G(') values at high frequency are also nearly identical to the osmotic pressures required to compress the casein dispersions. The rheology of sodium caseinate dispersions in which the caseins are not structured into micelles is also reported. Such dispersions have the behavior of associative polymer solutions at all the concentrations investigated, further confirming the importance of structure in determining the rheological properties of casein micelle systems.