Area-rule history is outlined in the wikipedia article.
The first mention is about a Nazi German engineer named Otto Frentzl in 1943. Theodor Zobel first mentioned area-rule in public
Various other Nazi-surplus engineers worked on area-rule when they moved to the USA after WW2 (Operation Paperclip): Dietrich Kuchemann, Adolf Busemann, etc.
Post WW2, American engineers Wallace D. Hayes and Richard T. Witcomb finally applied area-rule to the disappointing Convari F-102 Delta Dart. By re-contouring the fuselage into a "Kuchemann coke bottle"they able to reduce drag enough to achieve supersonic performance objectives. The improved Convair F-106 Delta Dagger first flew in 1956.
Early area-ruled airplanes often looked crude, with bulbous add-ons (e.g. Convair 880's Kuchemann carrots, bulbous rear fuselage in Buccaneer, lower aft fuel tank on EE Lightning).
Witcomb later went on to develop super-critical wings for trans-sonic airliners. While modern airliners may not immediately look like coke-bottle (from the side or top) they employ complex curvatures in wing root fillets, engine nacelles and aft fuselage profiles to smooth airflow at trans-sonic speeds. Please note that while airliners cruising at Mach 0.9 might not officially be trans-sonic, localized airflow might be. Witcomb's supercritical wings even out airflow to avoid localized super-sonic flow.
Modern fabrication methods are CAD design make area-ruling less obvious. For example, the Honda Jet uses a bulbous nose, quickly tapering under the fuselage before wings, then engines hang above the trailing edge .... all smoothing transitions in total airframe cross-section (area rule).
Trans-sonic airflow is a frightfully complex subject only vaguely related to sub-sonic, Newtonian physics. At one point, Witcomb realized that he was dealing with rigid, inflexible, "steel pipes" of super-sonic air that were difficult to bend around conventionally curved airframes. He jokingly described supersonic aerodynamicists as "pipe-fitters."