  The recent robust and homogeneous analysis of the world's supernova
distance-redshift data, together with cosmic microwave background and baryon
acoustic oscillation data, provides a powerful tool for constraining
cosmological models. Here we examine particular classes of scalar field,
modified gravity, and phenomenological models to assess whether they are
consistent with observations even when their behavior deviates from the
cosmological constant Lambda. Some models have tension with the data, while
others survive only by approaching the cosmological constant, and a couple are
statistically favored over LCDM. Dark energy described by two equation of state
parameters has considerable phase space to avoid Lambda and next generation
data will be required to constrain such physics.
