The failure process of concrete is a complex phenomenon in which the material inhomogeneities play an important role. Different ways of accounting for material disorder are commented on and examples are exhibited, showing the difficulties related to inhomogeneous material modeling. In a first part, results and limits via phenomenological probabilistic models (a probabilistic model of damage and a probabilistic numerical model of cracking) are pointed out. Then, results obtained on numerical simulations on lattices are studied. It is shown that the knowledge of the local disorder is a key factor for a better understanding of the global response (localization, size-effect, ...), even if these results can only be taken as qualitative ones. It appears that studies using numerical discrete models for concrete can lead to spurious results if the bias introduced by the discretization itself is not recognized and correctly accounted for. Finally it is shown with two examples (casted concrete and microcracked medium) how the structure of disorder can be identified and modelled. Some indications are given about the cases in which it seems useful to analyze the material at this micro-scale. The main interest seems to be their use for building phenomenological and material-related rules describing the response at a higher scale. The conclusion tries to separate the problems one has to treat in four main classes and to propose for each type of problem a better way to account for material disorder.