Directed sandpiles are particularly attractive examples of systems exhibiting the phenomenon of self-organized criticality. Their interest stems from the fact that, under certain assumptions, most of the exponents characterizing the models can be computed exactly. In this talk we will review the properties of generic directed sandpiles. By means of a combination of mean-field and field-theoretical methods, we will obtain a subset of ``exact'', universal exponents, valid for any directed sandpile, subject only to the condition of local and conservative toppling rules. The remaining exponents, model-dependent, can be on their turn expressed as a function of a single parameter. Our results are confirmed by means of large-scale simulations of two models: the standard directed Bak-Tang-Wiesenfeld sandpile, and a directed version of the Manna model, which we analyze for the first time.

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