Captivity started around 1870 in England
When five Beluga whales were the first cetaceans to be displayed
to the public

Later bottlenose dolphins and pilot whales were being kept
in places as the Battery aquarium, But they weren't really popular
Because of their sexual behaviour. Several stranded animals or
beluga whales were displayed now and then in English Aquariums till
some point in the 1800's.

In 1930 the Aquarium in Plymouth displayed some
beached animals for a while

True keeping of bottlenose dolphins as we know today
started in 1938, Marinestudios opened Marineland Florida
First only to record some underwater footage
untill the dolphins turned into a tourist attraction

Adolph Frohn, Became the first dolphin trainer in the world
when he discovered how easy dolphins can be taught to perform

Adolph Frohn working with 'Flippy'

Timeline

1954 Marineland Pallos Verdes California Opened, Displaying
two bottlenose dolphins born in Marine Studio's

1955 Miami Seaquarium displays Bottlenose Dolphins

1956 Forth Worth Zoological Park Texas Displays The
Amazon River Dolphin, Inia Geoffrensis

1957 Dolfinarium Harderwijk Displays Harbour Porpoises

1961 Chicago Zoological Park Displays Bottlenose

1963 New York Aquarium Displays Beluga

1965 Dolfinarium Harderwijk, Barcelona Zoo and
Zoo Duisburg Display Bottlenose Dolphins

1965Seattle Aquarium Displays Killer Whale Namu

1965 Enoshima Aquarium Displays Risso's Dolphins
and Bottlenose Dolphins (both species mated and produced hybrids)

1965 Marineland Pallos Verdes Displays Pilot Whales and
Pacific White-Sided Dolphins

1967Seaworld San Diego Displays Killer Whale Shamu

1968 Zoo Antwerpen Displays Bottlenose Dolphins and Tucuxi

1969 Flamingoland England Displays Bottlenose Dolphins
and Killer Whale

1969 Duisburg Zoo Displays Beluga's