Musicologists identify eras of classical music according to compositional and performance style. The predominant opinion as to these eras are as follows:
The Medieval era - 476-1400
The Renaissance era - 1400-1600
The Baroque era - 1600-1760
The Classical era - 1730-1820
The Romantic era - 1815-1910
The 20th Century era - 1900-2000
and The 21st Century era as anything from 2000 to the present.
There are certain composers who represent the compositional style of these eras most predominantly. These are as follows"
Medieval - Phillipe de Vitry, Guillaume de Machaut, Solage, Leonel Power and John Dunstaple.
Renaissance - Johannes Ockeghem, Josquin de Prez, Giovanni Pierluigi da Palestrina, William Byrd and Giovanni Gabrieli.
Baroque - Claudio Monteverdi, Jan Pieterzoon Sweelinck, Frescobaldi, Heinrich Schutz, Jean-Baptiste Lully, Dieterich Buxtehude, Archangelo Corelli, Henry Purcell, Alessandro Scarlatti, Francois Couperin, Tomaso Albinoni, Antonio Vivaldi, Georg Philipp Telemann, Jean-Philippe Rameau, Johann Sebastian Bach, Domenico Scarlatti, George Frideric Handel and Giovanni Battista Pergolesi.
Classical - Christoph Willibald Gluck, Carl Philipp Emanuel Bach, Luigi Boccherini, Joseph Haydn, Richard Haydn, Wolfgang Amadeus Mozart, Antonio Salieri, Ludwig van Beethoven, Johann Nepomuk Hummel and Franz Schubert.
Romantic - Carl Maria von Weber, Gaetano Donizetti, Niccolo Paganini, Giaocchino Rossini, Carl Loewe, Hector Berlioz, Johann Strauss I, Felix Mendelssohn, Frederic Chopin, Robert Schumann, Franz Liszt, Richard Wagner, Giuseppe Verdi, Jacques Offenbach, Clara Schumann, Bedrich Smetana, Anton Bruckner, Johann Strauss II, Johannes Brahms, Camille Saint-Seans, Pyotr Ilych Tchaikovsky, Antonin Dvorak, Edvard Grieg, Nikolai Rimsky-Korsakov, Edward Elgar, Giocomo Puccini, Gustav Mahler, Richard Strauss, Alexander Scriabin and Sergei Rachmaninoff.
20th Century - Claude Debussy, Arnold Schoenberg, Charles Ives, Maurice Ravel, Bela Bartok, Igor Stravinsky, Anton Webern, Edgard Verace, Alban Berg, Sergei Prokofiev, Heitor Villa-Lobos, Paul Hindemith, Carl Orff, George Gershwin, Aaron Copland, Kurt Weill, Dmitri Shostakovich, Elliott Carter, Olivier Messiaen, Samuel Barber, Benjamin Britten, Witold Lutoslawski, Leonard Bernstein, Iannis Xenakis, Gyorgy Ligeto, Luciano Berio, Pierre Boulez, Karlheinz Stockhausen, Krysztof Pendericki, Avo Part and Philip Glass,
There are of course transitions from one era into the next. For example, Beethoven and Schubert transitioned into the Romantic era, and Rachmaninoff transitioned into the 20th Century era. What is important is the musical styles, which predominated these eras. There's not one particular music style which predominated, but a person who is familiar with classical music should generally be able to listen to a piece and place it correctly into the era it belongs. There are of course exceptions. Some composers follow the styles of particular eras other than their own, for example, so their musical style may fit into one era, while their life is in another. Tchaikovsky was known to utilize themes from the classical era into his compositions. Mozart did the same with the Baroque era; so it's not always possible to listen to one piece without knowing its composer, and place it within a particular era. One should be able to listen to a Baroque piece, however, and be able to state the particular elements and styles, which make it Baroque as opposed to Romantic.