The Earth-Romulan War was a military conflict between the Romulan Star Empire and United Earth and its allies in the mid 22nd century. It was likely one of the key events that led to the foundation of the United Federation of Planets.
According to TOS "Balance of Terror", the Earth-Romulan War was fought with "primitive" nuclear weapons, and the two sides lacked ship-to-ship visual communications, so the combatants didn't even know what their enemies looked like. Eventually the two sides negotiated an armistice via subspace radio.
In all likelyhood the Enterprise (NX-01) participated in the war.
The Earth-Romulan War ended with the creation of the Neutral Zone between the Romulan Star Empire and what would become the Federation.