  We study whether a violation of the null energy condition necessarily implies
the presence of instabilities. We prove that this is the case in a large class
of situations, including isotropic solids and fluids relevant for cosmology. On
the other hand we present several counter-examples of consistent effective
field theories possessing a stable background where the null energy condition
is violated. Two necessary features of these counter-examples are the lack of
isotropy of the background and the presence of superluminal modes. We argue
that many of the properties of massive gravity can be understood by associating
it to a solid at the edge of violating the null energy condition. We briefly
analyze the difficulties of mimicking $\dot H>0$ in scalar tensor theories of
gravity.
