  We show that Hida's families of $p$-adic elliptic modular forms generalize to
$p$-adic families of Jacobi forms. We also construct $p$-adic versions of theta
lifts from elliptic modular forms to Jacobi forms. Our results extend to Jacobi
forms previous works by Hida and Stevens on the related case of half-integral
weight modular forms.
