What is negative refraction?

We will review the current status of various intrinsic definitions of negative refraction (i.e. negative phase velocity, or NPV, propagation which has been variously ascribed to counter-position of (i) the group velocity, (ii) the energy velocity, (iii) the Poynting Vector, with the wave vector of a plane wave in a medium. A key result is that simultaneously negative effective ε and μ can be achieved in a natural medium in motion. However, can this be said to result in observable phenomena? Recent progress in covariant methods has led to a more rigorous definition that is tied mathematically to what happens in the medium's rest frame. The challenge to produce a definition of NPV propagation that is not restricted to linear reference frames is also addressed. As well, progress has been made recently in clarifying the role of causality in deriving conditions for NPV propagation.