Origins
Some theorize that both Vulcans and Romulans are descendants of Sargon's people, who possibly colonized Vulcan some six million years ago. (TOS: "Return to Tomorrow") This theory, however, was later contradicted by the discovery of ancient humanoid progenitors. (TNG: "The Chase")
When Surak's reforms of embracing logical principles and rejecting emotions spread rapidly across Vulcan in the 4th century, a minority rejected Surak's ideals. They departed Vulcan in the 4th century; later, some of their descendants established settlements on the planets Calder II, Dessica II, Draken IV, Yadalla Prime and Barradas III, which might have become a center of this new offshoot civilization, called the Debrune, which later died out. (TNG: "Gambit, Part I")
At some point, another group settled on twin planets that became known as Romulus and Remus. While Romulus was an class M planet, Remus was a harsh planet notable only for its dilithium deposits. These two worlds were the foundation of an interstellar empire that expanded to many worlds, reaching across much of the Beta Quadrant. Eventually that power came to be known as the Romulan Star Empire. (TNG: "Gambit, Part I", "Gambit, Part II"; Star Trek Nemesis)
Physiology
Like Vulcans, Romulans have pointed ears, eyebrows that are arched and upswept, and copper-based blood that is green when oxygenated in the arteries, or copper or rust-colored when deoxygenated in the veins. (Star Trek Generations) Most Romulans have two brow ridges above the bridge of their nose, forming a V-shape on the forehead. However, a minority of Romulans lack these ridges, making them outwardly indistinguishable from Vulcans.
These "browless" Romulans appear to be confined to the 23rd century, from Mark Lenard's Romulan Commander in 2266 ("Balance of Terror") through Ambassador Nanclus in 2293 (Star Trek VI: The Undiscovered Country).
Despite their common ancestry there are also many subtle internal physiological differences between Vulcans and Romulans. This is evidenced in Dr. Beverly Crusher's failed attempt to treat a Romulan, Patahk, who had suffered advanced synaptic breakdown, with the methods used to treat Vulcans. (TNG: "The Enemy")
Romulans lack the rigorous mental disciplines developed by the followers of Surak. They are a passionate people, easily moved to extreme emotions. (TOS: "The Enterprise Incident")
This lack of mental discipline would seem to explain why Romulans lack the telepathic abilities that Vulcans possess.
There have been numerous instances of Romulans successfully mating with other species, as evidenced in Sela (Human/Romulan), Ba'el (Klingon/Romulan), and the grandfather of Simon Tarses (Human/Romulan). General Korrd indicates in a conversation with Caithlin Dar that Romulan women may have a unique anatomical makeup, although such comments are never substantiated. Star Trek V: The Final Frontier
A reference to Saavik being half-Romulan and half-Vulcan was cut from the final edit of Star Trek II: The Wrath of Khan. It was, however, mentioned in the novelization of Star Trek III: The Search for Spock.
While Vulcans possess much greater physical strength than most humanoids, it remains unknown if Romulans have superior strength to Humans.
The Terothka virus is a disease unique to Romulan physiology. Romulans are also susceptible to Tuvan Syndrome. (VOY: "Message in a Bottle"; DS9: "Inter Arma Enim Silent Leges")
See also
Romulan History @ Memory-Alpha.