  In this paper we study alternative tableaux introduced by Viennot. These
tableaux are in simple bijection with permutation tableaux, defined previously
by Postnikov . We exhibit a simple recursive structure for alternative
tableaux. From this decomposition, we can easily deduce a number of enumerative
results. We also give bijections between these tableaux and certain classes of
labeled trees. Finally, we exhibit a bijection with permutations, and relate it
to some other bijections that already appeared in the literature.
