Ball met Arnaz on 1940 while they filmed Rodgers and Hart and the stage production Too Many Girls.
Their bond was instantaneous and they eloped the same year to get married.
Ball filed for divorce in 1944, after she suspected that he was being unfaithful following nights he returned home drunk. However the couple turned things around and she dropped the proceedings against him.
The pair were actually six years apart in age at a time when it was not socially acceptable for an older women to marry a younger man, so they allegedly claimed that they were both born in the same year to avoid disapproval.
The couple had two children together Lucie Arnaz (1951) and Desi Arnaz Jr (1953).
They eventually divorced in 1960 after the reported pressures on Arnaz from alcoholism, womanising and managing his production company.
Source: Wikipedia and IMDB.