  I review the use of Type Ia supernovae (SNe Ia) in the 1998 discovery of the
accelerating expansion of the Universe, as well as the subsequent use of SNe Ia
to study the expansion history in more detail, determine the equation-of-state
parameter w, and measure the current value of the Hubble constant. This is the
lightly edited transcript of a lecture given at the Standard Model at 50
Symposium held at Case Western University, June 1-4, 2018, and thus corresponds
to the state of the field in mid-2018; however, a few post-symposium updates
were included in 2019. Also, this version includes at the end a brief update
(December 2023) on the early-time vs. late-time Hubble tension, which has now
reached a level of 5 sigma based on SNe Ia alone and is supported by several
other low-redshift determinations of the Hubble constant.
