Supernovae are one of the most established probes of the dark energy equation of state, w. However, in recent years, some of the most interesting cosmological results have focussed on tension between local measurements of the parameters sigma_8 and H_0 with the expected values of these parameters inferred from Planck measurements of the CMB assuming a Lambda-CDM cosmology. For both parameters, the tension is moderate, at the 2-3 standard deviation level, and may be due to unaccounted for systematic effects with any of the observations. However, the tension may represent the first hints of physics beyond LCDM. Motivated by this tension, in this talk, I’ll focus on new measurements of sigma_8 and H_0 with supernovae. I’ll start with a very brief overview of supernova cosmology, and then focus on how perturbations from peculiar velocities and gravitational lensing can put limits on sigma_8, using a signal which previously has been thought of as a nuisance. I’ll then focus on how Baryon Acoustic Oscillations can be used to calibrate supernovae, and provide a new way to measure H_0.