Western music is generally broken down into six periods. Each of these periods have certain characteristics which have shaped it and remained with it throughout its duration. However, lesser characteristics may change within any given period, and so you have works which fall into, say, the early Romantic period as opposed to the late Romantic.
The Medieval Period (400-1400)
Prior to about 900, nearly all the music we have any record of is a simple, one line structure called a plainchant. This was made up of one melodic line sung in unison by everybody. More complex music existed, but as it was secular and not sacred, we have very few, if any, written accounts of it.
Gradually, over the next 500 years, people began to expand on this simple structure by adding voices. At first, these voices sung a fixed interval1 above or below the original line. This was called an organum.
At some point, someone got the idea of having two different lines moving at the same time but not having a fixed interval. Usually the higher of these lines would be fairly florid, while the lower was a slower, pre-existing plainchant2.
By 1300, three and four voice compositions were being written. These works are referred to as polyphonic (many voices), to distinguish them from the monophony (single voice) of the simple plainchant.
The Renaissance (1400-1600)
By 1400 or shortly thereafter, several composers were writing polyphony in a slightly different way. Instead of using a slower bottom voice and faster upper voices, they made all voices equal in rhythmic variety. And instead of using four different chants, they used a single chant which was stated in each of the voices, upon their entrance, and the developed differently from one voice to the next. This led to a more unified sounding work, and gave rise to a number of contrapuntal (note-against-note) forms, such as the Canon (exact repetition in all the voices), the Canzon (a succession of themes, each developed and then discarded3), and the Fugue (one theme developed extensively).
Most of the development during this period was made in Italy. This is only natural as the Catholic church was the dominant force during this period, and was headquartered in Rome. Many of the best musicians wrote masses and other works for the church; nearly all of these works are in Latin, as this was the language used for services at the time. However, with the Reformation and rise of Protestantism in the latter half of the 16th Century, the nature of music had to change.
The Baroque Period (1600-1750)
One of the major changes in daily life around 1600 was the switch from the Catholic church to various Protestant religion4. The result of this change was that the language of the services switched from Latin to German. Because most people had not spoken Latin, the masses could be as ornate as the composer desired. But if the language was understandable by the majority of the people, the music should be simple enough that they could understand the words. As a result, the Catholic Latin mass was no longer needed, but new German services were. New hymns (chorales) were written to provide music for these services. These were primarily homophonic (simple chordal structure) in nature, contrasting with the polyphony that continued in instrumental and Latin works.
By the mid-1700s, polyphony had reached its peak. Several composers began to explore simpler styles of composition, such as symphonies and concertos, which had been foreshadowed in preludes, partitas, and other non-polyphonic forms of the Baroque period. This, along with a gradual secularisation of music, led to the Classical period.
The Classical Period (1750-1800AD)
This is a rather curious period in musical history. Very little was done to change the basic musical language, aside from the abandonment of polyphony. The major contribution during this period was the enlargement of many aspects of music. The orchestra was developed, the opera was made into a more continuous work, and the level of complexity in writing was reduced somewhat. However, this brief period introduced a more virtuositic style of playing on many instruments, and set the stage for a major harmonic expansion during the next century.
The Romantic Period (1800-1900AD)
The shift from the Baroque to the Classical had resulted in a change of thought from the horizontal (polyphony and the sense of line) in music to the vertical (chordal structure). The romantic period led to a massive enlargement in what was acceptable as far as chordal progressions went. By the middle of the 19th Century, composers had begun to 'borrow' chords that technically should not have been used in the way they were5. This resulted in a breakdown of tonality, and by the later part of the period, nearly any chord could be used with very minimal preparation. Modulations to distant keys were sudden and severe.
The scale of works also continued to expand. By the end of the century, massive operas of three or more hours were being written; symphonies of an hour and a half were common, and perhaps 200 or more players would be needed to perform these titanic works. Everything seemed to be getting bigger; even chamber works were of a scale only dreamed of before.
The 20th Century
By 1900, something had to happen to change music. Several things did, all of which had a pronounced effect on the next 100 years of writing.
Firstly, popular and 'classical' music began to separate. Jazz, and then Rock, became the music of the masses, and classically-trained composers found themselves without the numbers of listeners that their predecessors had enjoyed. Secondly, many composers abandoned the idea of a tonal centre, consonance, or harmonic progression altogether, resulting in atonality, dissonance, and free use of borrowed chords becoming common. And eventually, the 'classical' world fractured into many different groups, most of which began to write much smaller pieces again. Some would even revolt against the preciseness of notation that many Romantic composers prided themselves on, leaving some or all aspects of their works to chance.
No prominent school of thought has yet arisen to claim that it is the true 20th Century descendant of Romanticism. As such, many scholars think that the 20th Century Period will continue until the middle of the 21st Century.