  We show that the $\mathscr{B}$-free subshift $(S,X_{\mathscr{B}})$ associated
to a $\mathscr{B}$-free system is intrinsically ergodic, i.e.\ it has exactly
one measure of maximal entropy. Moreover, we study invariant measures for such
systems. It is proved that each ergodic invariant measure is of joining type,
determined by a joining of the Mirsky measure of a $\mathscr{B}'$-free subshift
contained in $(S,X_{\mathscr{B}})$ and an ergodic invariant measure of the full
shift on $\{0,1\}^{\mathbb{Z}}$. Moreover, each ergodic joining type measure
yields a measure-theoretic dynamical system with infinite rational part of the
spectrum corresponding to the above Mirsky measure. Finally, we show that, in
general, hereditary systems may not be intrinsically ergodic.
