Morphology is the study of the internal structure of words. A vigorous ongoing debate surrounds the question of how such internal structure is best accounted for: by means of lexical entries and deterministic symbolic rules, or by means of probabilistic subsymbolic networks implicitly encoding structural similarities in connection weights. In this review, we separate the question of subsymbolic versus symbolic implementation from the question of deterministic versus probabilistic structure. We outline a growing body of evidence, mostly external to the above debate, indicating that morphological structure is indeed intrinsically graded. By allowing probability into the grammar, progress can be made towards solving some long-standing puzzles in morphological theory.