7 'The Queen's Gambit' (2020)An Orphan's Rise to GeniusNetflixLike Anne with an E, Netflix's The Queen's Gambit is a period drama built around an orphan finding her way. 4 'Downton Abbey' (2010–2015)Upstairs, Downstairs, and Everything BetweenFocus FeaturesAnother period drama to watch is 2010's Downton Abbey, which needs little introduction. The show has become one of Netflix's biggest hits, breaking viewership records with its irresistible blend of period drama and modern storytelling. Billed as part family drama and part frontier survival story, it has already been renewed for a second season. Billed as part family drama and part frontier survival story, it has already been renewed for a second season.