  The theory of overconvergent modular symbols, developed by Rob Pollack and
Glenn Stevens, gives a beautiful and effective construction of the $p$-adic
$L$-function of a modular form. In this paper, we give an analogue of their
results for Bianchi modular forms, that is, modular forms over imaginary
quadratic fields. In particular, we prove control theorems that say that the
canonical specialisation map from overconvergent to classical Bianchi modular
symbols is an isomorphism on small slope eigenspaces of suitable Hecke
operators. We also give an explicit link between the classical modular symbol
attached to a Bianchi modular form and critical values of its $L$-function,
which then allows us to construct $p$-adic $L$-functions of Bianchi modular
forms.
