Parallax is still the foundation of stellar distance measurement, but it's just the first rung on a ladder that astronomers use depending on how far away a star is. The basic idea is simple: as Earth orbits the sun, nearby stars appear to shift position slightly against the distant background. Measure that shift, do the geometry, and you've got your distance. The European Space Agency's Gaia mission, which has been collecting data for years now, has made parallax measurements incredibly precise - we're talking about detecting shifts smaller than a human hair viewed from miles away.
For stars too distant for parallax to work well (anything beyond a few thousand light-years or so), astronomers rely on other methods. They use something called a "standard candle" - objects like certain types of supernovae or variable stars where they know the actual brightness. By comparing how bright those objects appear from Earth versus their known true brightness, they can calculate distance. Another approach uses spectroscopy to determine a star's type and temperature, then cross-reference that with similar stars whose distances we already know. These methods chain together; the closer stars measured by parallax help calibrate the brightness of standard candles, which then lets us measure stars way beyond the solar neighborhood.
So for Sirius, parallax works perfectly well - it's one of the nearest stars to us. Betelgeuse is trickier because it's much farther out, so astronomers combine parallax data with other techniques to nail down its distance. The methods haven't fundamentally changed since the 2000s, but the precision and the quality of data have improved dramatically thanks to better satellites and instruments.