Neurons in the primary visual cortex (V1) of rodents are selective to the orientation of the stimulus, as in other mammals such as cats and monkeys. However, in contrast with those species, their neurons display a very different type of spatial organization. Instead of orientation maps they are organized in a “salt and pepper” pattern, where adjacent neurons have completely different preferred orientations. This structure has motivated both experimental and theoretical research with the objective of determining which aspects of the connectivity patterns and intrinsic neuronal responses can explain the observed behavior. These analysis have to take into account also that the neurons of the thalamus that send their outputs to the cortex have more complex responses in rodents than in higher mammals, displaying, for instance, a significant degree of orientation selectivity. In this talk we present work showing that a random feed-forward connectivity pattern, in which the probability of having a connection between a cortical neuron and a thalamic neuron depends only on the relative distance between them is enough explain several aspects of the complex phenomenology found in these systems. Moreover, this approach allows us to evaluate analytically the statistical structure of the thalamic input on the cortex. We find that V1 neurons are orientation selective but the preferred orientation of the stimulus depends on the spatial frequency of the stimulus. We disentangle the effect of the non circular thalamic receptive fields, finding that they control the selectivity of the time-averaged thalamic input, but not the selectivity of the time locked component. We also compare with experiments that use reverse correlation techniques, showing that ON and OFF components of the aggregate thalamic input are spatially segregated in the cortex.