Observations of type Ia supernovae (SN Ia) play a starring role in two cosmological surprises: the accelerated expansion of the Universe driven by dark energy and the discrepancy between the measured and inferred Hubble constant from the late and early Universe. I will describe the contemporary use of SN Ia to measure cosmological distances, with an emphasis on the limiting factors in their application. With ongoing and upcoming surveys, we are passing a threshold beyond which systematic uncertainties limit the cosmological utility of SN Ia. However, as the number of SN Ia we can study grows, and we broaden the way we study them, we are also gaining new insights that we can apply to the problem. I will describe recent advances in our understanding of the progenitors and explosions of SN Ia and their correlations with their host-galaxy and larger-scale environments that are pointing the way make better use of SN Ia samples in measuring the Hubble constant and the properties of dark energy.