The preprint `Representable multicategories' is available at http://www.maths.usyd.edu.au:8000/u/hermida Abstract: We introduce the notion of representable multicategory, which stands in the same relation to that of monoidal category as fibration does to contravariant pseudofunctor (into Cat). We give an abstract reformulation of multicategories as monads in a suitable Kleisli bicategory of spans. We describe representability in elementary terms via universal arrows. We also give a doctrinal characterisation of representability based on a fundamental monadic adjunction between the 2-category of multicategories and that of strict monoidal categories. The first main result is the coherence theorem for representable multicategories, asserting their equivalence to strict ones, which we establish via a new technique based on the above doctrinal characterisation. The other main result is a 2-equivalence between the 2-category of representable multicategories and that of monoidal categories and strong monoidal functors. This correspondence extends smoothly to one between bicategories and a localised version of representable multicategories. -- Claudio Hermida School of Mathematics and Statistics F07, University of Sydney, Sydney, NSW 2006, Australia