  Classical Cepheids were the first stellar standard candles and have played a
crucial role for astronomical distance measurements ever since the discovery of
the Leavitt law (period-luminosity relation). Enormous improvements in distance
accuracy have been achieved since Hertzsprung's first application of Leavitt's
law to measure the distance to the Small Magellanic Cloud in 1913, notably in
very recent years thanks to a large data set of highly accurate space
astrometry from the ESA mission Gaia. Complemented by homogeneous space
photometry, Cepheids enable the most accurate distance estimates to galaxies
hosting type-Ia supernovae up to approximately 70 Mpc distant. Here, I review
the history of Cepheid distance measurements, open questions on the side of
stellar astrophysics, and recent studies seeking to quantify and mitigate
systematics with a view to further improve the accuracy on the Hubble constant.
For example, the recently launched James Webb Space Telescope will enhance
precision due to 4x lower sensitivity to source blending in crowded regions and
greater sensitivity in dust-insensitive infrared bands. Future 30m-class
telescopes could in principle further improve Cepheid distance measurements
towards the Hubble flow, if technical challenges related to a continuously
evolving instrument can be overcome.
