The first machine recording voice was called phonograph. It was developed as a result of Thomas Edison's work on two other inventions: the telegraph and the telephone. Edison was working on a machine that would transcribe telegraphic messages on paper tape, which could later be sent over the telegraph repeatedly. This development led Edison to speculate that a telephone message could also be recorded in a similar fashion. He experimented with an embossing point which was held against moving paraffin paper. The mechanical vibrations arised from speaking made indentations in the paper. Edison later changed the paper to a metal cylinder with tin foil. The machine had two units, one for recording, and one for playback. When one would speak into a mouthpiece, the sound vibrations would be indented onto the cylinder by the recording needle in a vertical direction. Edison tested the machine by speaking the nursery rhyme, "Mary had a little lamb." To his amazement, the machine played his words back to him. The patent on the phonograph was issued on February 19, 1878. The invention was not quite original. Similar machine was invented by French "blessed" poet and scientist Charles Cros in 1877, but it was only a theory, since he did not produce a working model of it (and more: his envelope with the invention was in the French Academy of Sciences opened as long as a several months after delivery). On January 24, 1878 the Edison Speaking Phonograph Company was established. Edison received $10,000 for the manufacturing and sales rights and 20% of the profits.

The original Edison's phonograph and "Edison's home phonograph"
(from http://memory.loc.gov/ammem/edhtml/edcyldr.html)

But Edison did not further work on the phonograph for a while, concentrating instead on inventing the light bulb. And so others moved forward to improve on his invention, including Chichester A. Bell and Charles Sumner Tainter, who developed a wax cylinder for the phonograph. In 1887 Edison resumed work on his phonograph and used wax cylinders too. This early cylinders had two significant problems. The first was the short length of the cylinders, only 2 minutes. The second problem was that no mass method of duplicating cylinders existed.

Today we know, that Edison 's phonograph was only "closed street". In 1895 "new" man revolutionised the future of recorded sound. His name was Emile Berliner. He came to Washington in 1870 from Germany. Berliner's gramophone - how he called his "speaking machine" - differed its contemporaries in that it used a flat disc to record sound rather then the cylinder proposed by Edison. The disc permitted mass duplication and playing time was 4 minutes. No longer was music available on fragile cylinders. Berliner's gramophone were acquired by the Victor Talking Machine Company (eventually RCA). In 1897 he founded Deutsche Gramophon and one year later Britain's Gramophone Co. in Europe. His trademark, later adopted by RCA, was a painting of his dog Nipper, listening to "his master's voice". Paper labels with this trademark appeared in 1900.

Fully functioning replica of the original Berliner's gramophone
(from http://www.phonographs.com/berliner.htm)

Some time Edison followed in offering his cylinder phonographs. But after 1905, discs and disc players began to dominate the market. Edison was forced to produce disc phonographs. But his disc phonograph and his discs were incompatible with other discs or disc players (for example he used mentioned vertical-cut method for recording grooves on contrary Berliner's and today's horizontal-cut method) . . .

The first disc recorded by electrical equipment was produced in 1920, gramophones turned by electricity (instead spring motors) we know from 1925. First longplaying discs (knows as LP's) appeared in 1904, but only from 1931 its were produced with standard speed 33.3 r.p.m. The shellac discs, which was too breakable,  were replaced in 1946 by plastic ones. The author of micro-grove's disc is Peter Goldmark (1948). This micro-discs with 45 r.p.m. in short time  pushed away old discs with 78 r.p.m.