  We use the supergeometric formalism, more precisely, the so-called "big
bracket" (for which brackets and anchors are encoded by functions on some
graded symplectic manifold) to address the theory of Jacobi algebroids and
bialgebroids (following mainly Iglesias-Marrero and Grabowski-Marmo as a
guideline). This formalism is in particular efficient to define the
Jacobi-Gerstenhaber algebra structure associated to a Jacobi algebroid, to
define its Poissonization, and to express the compatibility condition defining
Jacobi bialgebroids. Also, we claim that this supergeometric language gives a
simple description of the Jacobi bialgebroid associated to Jacobi structures,
and conversely, of the Jacobi structure associated to Jacobi bialgebroid.
