Variations of the total solar irradiance (TSI) over long periods of time provide natural Earth-climate forcing and are thus important to monitor. Variations over a solar cycle are at the 0.1 % level. Variations on multi-decadal to century timescales are (fortunately for our climate stability) very small, which drives the need for highly-accurate and stable measurements over correspondingly long periods of time to discern any such irradiance changes. Advances to TSI-measuring space-borne instruments are approaching the desired climate-driven measurement accuracies and on-orbit stabilities. I present a summary of the modern-instrument improvements enabling these measurements and present some of the solar-variability measurement results from recent space-borne instruments, including TSI variations on timescales from solar flares and large-scale convection to solar cycles.