Romantic Period is the third period of music (European) which I am exposed to, where repertoires in this period were composed between 1815 to 1910. For a more detailed historical background of repertoire created during this period can be found here: http://en.wikipedia.org/wiki/Romantic_music
To play music of this period, we need to take note of the following:-
1. The sustain pedal is invented as pieces is usually played using a piano or organ. Hence, there is a heavy use of pedal to create the necessary mood. Because of that, trills are not used to extend a note. The pedal is used instead.
2. Pieces in this period is usually more expressive and emotional. There is a need to use a greater range of dynamics, long crescendos and decrescendos. And the piano used in this period are capable of delivering a much bigger range of dynamics.
3. Usually more complex patterns than Baroque and Classical periods.
4. Greater flexibility, allows rubato to bring out the emotive and increase the expressions.