While both downloadable and disc-based Xbox 360 and original Xbox games work on Xbox One and Xbox Series X, only selected games are supported on a case-by-case basis. Though Microsoft wound down its original Xbox and Xbox 360 back compatible efforts in mid-2019 in favour of Xbox One support for Xbox Series X - which also supports a range of improvements - there was one final update in November 2021 as part of Xbox's 20th anniversary celebrations, adding another 76 games and adding additional enhancements to existing ones.
Xbox backwards compatibility of Xbox 360 games was Microsoft's big surprise back at E3 2015, and since debuting the feature later that year, the publisher rolled out new releases on a month-by-month basis.