  We study the constraints coming from local causality requirement in various
$2+1$ dimensional dynamical theories of gravity. In topologically massive
gravity, with a single parity non-invariant massive degree of freedom, and in
new massive gravity, with two massive spin-$2$ degrees of freedom, causality
and unitarity are compatible with each other and both require the Newton's
constant to be negative. In their extensions, such as the Born-Infeld gravity
and the minimal massive gravity the situation is similar and quite different
from their higher dimensional counterparts, such as quadratic (e.g.,
Einstein-Gauss-Bonnet) or cubic theories, where causality and unitarity are in
conflict. We study the problem both in asymptotically flat and asymptotically
anti-de Sitter spaces.
