Refrigeration was demonstrated by a Scotsman (of course!) in the 1700s, but the first practical refrigerator wasn't built until an American did it in 1834. Read about it here
Archeologists have found remains of ice pits from the seventh century BC, and references suggest that ice pits and ice houses were in use before 1100 BC.
Oliver Evans is credited as the inventing it by designing the first artificial refrigerator, using vapur instead of liquid, although he never actually built one.