Boosting combines weak classifiers to form highly accurate predictors. Although the case of binary classification is well understood, in the multiclass setting, the ``correct'' requirements on the weak classifier, or the notion of the most efficient boosting algorithms are missing. In this paper, we create a broad and general framework, within which we make precise and identify the optimal requirements on the weak-classifier, as well as design the most effective, in a certain sense, boosting algorithms that assume such requirements.