BuddyPress 5.0.0 will require WordPress 4.7 or greater. See https://buddypress.trac.wordpress.org/ticket/8025, as well as the perennially ripping read, https://codex.buddypress.org/getting-started/wordpress-version-compatibility/.
BuddyPress 4.1.0 is ready for download: https://buddypress.org/2018/12/buddypress-4-1-0-maintenance-release/
BuddyPress 4.0.0 “Pequod”: https://buddypress.org/2018/11/buddypress-4-0-0-pequod/
BuddyPress 4.0.0 RC 1 is now available: https://buddypress.org/2018/11/buddypress-4-0-0-release-candidate-1/
4.0.0 stable is currently scheduled for Tuesday, November 27.
BuddyPress 3.1.0 is now available. It includes 23 bug fixes. See https://buddypress.org/2018/06/buddypress-3-1-0-maintenance-release/ for more information.
Note that there may be some manual adjustments you will need to make to fix some outstanding issues.
BuddyPress 3.0.0 “Apollo” is now available for immediate download from the WordPress.org plugin repository, or right from your WordPress Dashboard.
Read all about it at https://buddypress.org/2018/05/buddypress-3-0-0-apollo/
Check out the changelog for more information https://codex.buddypress.org/releases/version-3-0-0/
BuddyPress 2.9.3 is released: https://buddypress.org/2018/01/buddypress-2-9-3-security-and-maintenance-release/