Looking primarily at the Western European/North American experience, named roads seem to arise when a settlement has 8-12 roads to be distinguished from each other. I mapped a number of small settlements in the American West in the early 2000s that still did not have named streets; residents got their mail at a central post office and knew nearly everyone in town and where their houses were. Today, E-911 systems have spurred county governments to assign city-style addresses to all dwellings.

At least in the Anglo-American tradition, road names generally and organically arise from the descriptive: the London Road, the High (or Main) Street, the Church Street, Warleggan's New Street, Poldark's Close. Over time, specific articles and possessives melt away into the names that sound right to modern English speakers. Only government- or patron-sponsored new towns or the large new additions resulting from 19th century urban growth prompted naming schemes (such as trees) for whole groups of streets.

Japan, and probably other places as well, uses a cellular scheme in which almost no roads have names, except that each district will probably have a Chuo-Dori (Main Street). Instead, each subdistrict has a number, and each block within that subdistrict has a logical number. Building numbers on each block may be logical, or may be chronological. That's why the corner police box will nearly always display a large-scale map of the immediate area.

Western-style addresses are still the exception rather than the rule in most of the world. Companies promoting new addressing and geolocation schemes, such as What3Words, estimate that 4 billion people worldwide have no address for mailing purposes.

House numbers were introduced in some large European cities in the 18th century for various reasons of taxation and government administration: in various towns in Prussia in 1737, in Madrid circa 1750, in Trieste in 1754, in Paris (by a directory publisher) in 1779. London’s regulations on house-numbering date from the 1760s; Vienna’s scheme from the 1770s. Numbering was often done to aid the billeting of soldiers, and there is some evidence that British troops gave numbers to New York houses during the American Revolution. It seems likely that these were soon removed by resentful property owners. However, this webpage from the New York Public Library indicates that New York and Philadelphia both had houses numbered by 1785, so New Yorkers may well have found the numbers useful, rather than merely unwelcome reminders of an occupying army.

The modern scheme that we know, of even numbers on one side and odd on the other, and of numbering based on a distance-based scheme rather than mere ordinals, both appear to have originated in Philadelphia in time for the 1790 Census. The logical technique of having house numbers relate to numbered streets—2801 being on the corner of 28th Street—also originated in Philadelphia in 1856 and was still called the “Philadelphia system” when Chicago switched to it in 1879. (Manhattan and San Francisco never adopted such schemes.)

Literature on house-numbering is scarce, but there’s a good bibliographic section on a webpage called The Gallery of House Numbers. Alas, most of the academic papers there cited are behind academic publisher paywalls, but you can read this useful historical review by Reuben Rose-Redwood of the University of Victoria.