Little Boy was a simple U-235 "gun-type" design, Fat Man a Pu-239 hollow-pit implosion, but without any booster.
Modern warheads are all Pu-239, and it is believed all nuclear powers, even the minor ones, have mastered boosting - a few grams of tritium and deuterium gas inside the hollow pit, that fuses under the pressure generated by the initial burst of fission, yielding a small number of 14 MeV "hard" fusion neutrons to catalyse further fission.
Only a few powers (US, France, Britain, Russia, China and India) have gone on to develop "true" three-stage H-bombs, using lithium deuteride secondaries "downstream" of the primary pit.
(None of that is classified, I never held a clearance high enough to see the details!)
