As the name itself suggests, the drama tells the story of an atypical family indeed. Bok Gwi-joo (Jang Ki-yong) and his family are unique, each possessing supernatural abilities. Gwi-joo has the power to travel back in time, but only to revisit happy moments of his life. However, he’s unable to alter the past, leaving him trapped. Unfortunately, this constant dwelling plunges him into depression, causing him to lose his unique ability. Similarly, his family members also find themselves grappling with ‘modern-day’ problems like insomnia, bulimia, and smart-phone addiction, which ultimately result in the loss of their own supernatural abilities. Enter Do Da-hae (Chun Woo-hee), who unexpectedly—or, expectedly—becomes intertwined with this extraordinary family. Despite learning their secrets, she decides to live with them for her own reasons, unknown. With her cheery presence in their lives, a gradual transformation begins to take place in the family.