Hurricane Greta, later Hurricane Olivia, was one of fourteen named Atlantic hurricanes to cross over Central America into the eastern Pacific while remaining a tropical cyclone. The seventh named storm of the 1978 Atlantic hurricane season, Greta formed from a tropical wave just northwest of Trinidad on September 13, and despite being in a climatologically unfavorable area, gradually intensified while moving west-northwestward. On September 16, it became a hurricane south of Jamaica. Two days later, the well-defined eye approached northeastern Honduras but veered to the northwest. After reaching peak winds of 130 mph (210 km/h) that day, Greta weakened while paralleling the northern Honduras coast just offshore. On September 19, it made landfall on Belize near Dangriga and quickly weakened into a tropical depression while crossing Guatemala and southeastern Mexico. After entering the eastern Pacific, the system re-intensified into a hurricane and was renamed Olivia, the eighteenth named storm of the 1978 Pacific hurricane season which weakened before landfall and dissipated over Chiapas on September 23.

The 1978 Atlantic hurricane season was a slightly above average hurricane season in terms of number of named storms. Eleven tropical cyclones were named in all, and five of these became hurricanes; two of the five became a major hurricane. This was also the last Atlantic hurricane season to use an all-female naming list. The season officially began on June 1, 1978, and ended on November 30, 1978. These dates, adopted by convention, denote the period in each year when most tropical cyclogenesis occurs in the Atlantic basin. However, the formation of subtropical or tropical cyclones is possible at any time of the year, as shown by the formation of an unnamed subtropical storm on January 18.