The relationship between Fallon Carrington and Jeff Colby began in high school, prior to I Hardly Recognized You. They became business partners later in life and founded Morell Green Energy Corporation together. Their business relationship soon turned to a romantic one, however with nefarious intentions as Jeff was attempting to get revenge on the Carringtons.
Jeff and Fallon entered into a ruse marriage in Our Turn Now, each one scamming the other; however, Fallon ultimately won and used a technicality to cancel out her marriage while taking twenty-five percent of his company - leaving him bitter.
It was then revealed in A Line From the Past that Jeff has Carrington blood, as his grandmother had an affair with Tom Carrington, which makes him Fallon Carrington's cousin; which also explains why Blake was so uncomfortable with them ever persuing a romantic relationship.
As of this revelation, Jeff and Fallon are civil and friendly.