At the turn of the century our perspective was limited to the universe of stars in the Milky Way, and our dreams only ranged as far as probing the arrangement of objects therein. Accurate distances to nearby stars could only be measured by using the Earth's motion around the Sun, which causes a slight change in an object's apparent position with respect to the more distant background. This shift, called the parallax, was only observable out to distances of a few hundred light-years—scarcely enough to make out that our Sun was part of an elongated structure, which would later turn out to be a spiral arm.

One of the chief astronomical mysteries of this era was the nature of nebulae. These fuzzy blurs of light seemed ubiquitous, and had wildly diverse shapes ranging from elegant spiral structures to irregular blobs. A few of them (globular clusters associated with our galaxy) could be resolved into individual stars at their edges, but most could not. The first astronomer to observe many of these objects with a powerful telescope was William Herschel, who formed the opinion that many nebulae were objects similar to our own galaxy, but viewed from a great distance. Most astronomers, reluctant to introduce thousands of "island universes" into their world view, preferred to assume that the nebulae must be gaseous structures within our own galaxy. Many of the irregular nebulae were later associated with stars; today we know these as supernova remnants and planetary nebulae. The nature of the beautiful spiral nebulae, however, remained a riddle for more than a century after Herschel completed his work in 1802.

Our ability to measure astronomical distances took a great leap forward with Henrietta Leavitt's pioneering work on variable stars in 1912. She discovered numerous Cepheid variables (stars whose luminosities vary according to a regular and distinctive pattern) in the Small Magellanic Cloud (SMC), and obtained enough data on twenty-five stars to measure their periods and peak luminosities. There turned out to be a surprisingly strong correlation between these two variables, one which promised a new and better astronomical yardstick. By observing a new Cepheid variable for a long time and measuring the period of its variation, its luminosity could be inferred. The star's apparent brightness would then allow astronomers to determine its distance, at least relative to the SMC. (For example, one could find that a new Cepheid was 2.3 times farther away than the SMC, but its absolute distance could still not be determined.) Unfortunately, there were no Cepheid variables close enough to the Sun to have an observable parallax; this technique therefore suffered from a large uncertainty in the stars' intrinsic luminosities. The first Cepheid parallaxes were not measured until quite recently (e.g. Feast & Catchpole 1997), and required the launching of a special satellite to obtain.

The work of Leavitt made possible the first distance measurements for the Magellanic clouds, but these remained rather inaccurate until other techniques were developed. Cepheid distances were calibrated with reasonable accuracy for the first time by Harlow Shapley between 1914 and 1918, who used them to measure the distances to nearby globular star clusters. His work set the scale of the Milky Way to about 300,000 light-years—ten times larger than any previous estimate! Ironically, this result convinced Shapely that the spiral nebulae must be part of our galaxy. If they were "island universes" of similar scale, he reasoned, they would have to lie at even larger (and apparently inconceivable) distances to achieve their apparent uniformity. The debate on the nebulae raged on for several years, despite growing spectroscopic evidence that they were composed of stars.

The controversy was finally settled by Edwin Hubble's work, which began with his discovery of a Cepheid in the Andromeda nebula. With the help of Shapley's calibration he calculated a distance of 900,000 light-years, which was clearly extragalactic. He was later able to find Cepheids in the outskirts of other nebulae, and painstakingly estimated distances and luminosities for a few other nearby galaxies. By comparing these results to the luminosities of more distant nebulae of similar appearance, he eventually arrived as distance estimates for forty-five objects. He also had measurements of their velocity relative to the Sun, by attributing a frequency shift in their spectra to the Doppler effect. The discovery that all these nebulae were receding, and at a rate proportional to their distance, astounded the astronomical community. The correlation v=H₀d quickly became known as Hubble's Law, and the constant H₀ was dubbed Hubble's Constant.

In 1929 Hubble published a summary of hs research and transformed the science of astronomy in two important ways. First, by measuring the distances to many nebulae he was able to determine once and for all that they were extragalactic objects. Given the enormous distances involved, it became clear that their luminosities could only be explained by the galaxy hypothesis: each nebula was made up of billions of stars. Our cosmic world-view jumped from that of an isolated swarm of billions of stars, to that of an expansive universe with billions of galaxies. Second, the discovery of Hubble's Law quickly led to the idea that the universe itself was expanding. Hubble's paper thus marked the simultaneous birth of extragalactic astronomy and evolutionary cosmology as distinct fields of research. Cosmology, as a science, is only seventy-five years old!