Rom is the son of Keldar and Ishka, younger brother of Quark, and father of Nog. A failure as a businessman but a mechanical genius, he worked as a waiter for several years at Quark's on Deep Space 9 before becoming an engineer in the Bajoran Militia. He eventually succeeded Zek as Grand Nagus of Ferenghinar.

As a child, Rom was always teased for having smaller-than-average lobes than the rest of the boys. Quark was the worst, telling everyone that Rom was adopted. On Rom's Naming Day, Quark substituted his brother's presents with old vegetables, and sold the presents for more than their father had paid for them, which actually earned him the praise of his parents.
(DS9: "Rivals")

When Rom was a child he had a latinum tooth sharpener.
(DS9: "Family Business")

In the early-2350s, Rom met his first wife, Prinadora. He signed a standard five-year marriage contract with her father in order to have a child. In 2353, they had their son, Nog. Rom, however, then fell in love with Prinadora and wanted to extend the contract. Unfortunately, he was so in love, that he never bothered to read the extension before signing it. In the end, her father swindled Rom out of all his money, and Prinadora left Rom (and Nog) for a richer man.
(DS9: "Doctor Bashir, I Presume")

Quark exploited and belittled Rom all of his life. Growing up, Quark often teased Rom about his smaller lobes and about supposedly being adopted. He worked in Quark's bar for low wages, and was cheated out of his share of the profits.

When Grand Nagus Zek visited Deep Space 9, Quark made Rom give up his quarters for the Nagus. When Zek appointed Quark to be the new Grand Nagus, Rom conspired to kill Quark, and may have succeeded if Zek and Odo hadn't arrived at the last moment. Quark later praised Rom for his treachery.
(DS9: "The Nagus")

He opposed Quark over his treatment of their mother, who against Ferengi law earned profit. He refused to allow Quark to stop his son Nog's admission to Starfleet Academy in late 2371.
(DS9: "Heart of Stone")

The following year, he single-handedly organized a union of Quark's employees after Quark had cut their wages. He defied his brother and Liquidator Brunt, who the Ferengi Commerce Authority had sent to resolve the situation. After the wages had been restored, Rom made the final break with his brother. Rom joined the maintenance crew on Deep Space 9.
(DS9: "Bar Association")

In 2373, Rom fell in love with Leeta, a Bajoran woman who worked as a dabo girl at Quark's.
(DS9: "Let He Who Is Without Sin...")

Despite constantly planning to do so, Rom could never work up the courage to ask Leeta out. Finally he Rom stopped her leaving the station and confessed his love for her. Leeta her love also and remained.
(DS9: "Doctor Bashir, I Presume")

The two were married in late 2373 in a ceremony officiated by Benjamin Sisko.
(DS9: "Call to Arms")

A series of events through the years all contributed to Rom's elevation to nagus. In 2375, Rom eventually became Grand Nagus of the Ferengi Alliance.

At first Grand Nagus Zek ignored Rom, believing him to be of poor business sense and not very intelligent. Zek disagreed strongly with many of Rom's choices concerning his son Nog.
(DS9: "The Nagus")

Rom helped restore the Nagus to the Ferengi ways after the Nagus had been influenced by the wormhole aliens. He, along with Quark, took the Nagus back to the wormhole and was successful in persuading them to restore Zek back to his old self. He helped restore Zek as the Grand Nagus after Brunt had deposed him.
(DS9: "Prophet Motive", "Profit and Lace")

When Ishka became Zek's companion, she influenced him in trying to turn the Ferengi society into a more tolerant one that allowed free commerce and woman's rights. Her influence over Zek led to social reform and a Ferenginar that instituted democratic changes. Rom became the perfect choice for Nagus because he himself had never been a traditional Ferengi.
Zek believed that he would be an excellent successor for the newly reformed Ferenginar.
(DS9: "The Dogs of War")