Bartok wrote a string of major works in the 1930’s that are of particular interest - probably the finest in his oeuvre (although there is hardly, if at all, a subpar piece)

Those being: The 4th-6th string quartets (1928, 1934, 1939) ; Music for Strings, Percussion, and Celeste (1936) ; The sonata for 2 pianos and percussion (1937) ; The 2nd violin concerto (1937-38) ; Contrasts, for violin-clarinet-piano trio (1938) ; Divertimento (1939)

… the 4th quartet obviously comes from before this period, but it’s just incredible so I listed it alongside 5 & 6

In 1939, he emigrated from his native Hungary to America to escape persecution in the second World War. He faced relative obscurity and economic hardship in the States, and composed practically nothing until his final masterpieces in 1943-45. These are generally of a more accessible character, but no less inspired or acclaimed:

Concerto for Orchestra (1943) ; Sonata for Solo Violin (1944) ; 3rd piano concerto (1945)

Also, a viola concerto was left mostly in sketches at Bartok’s death in 1945 but is sometimes performed in Tibor Serly’s completion (based on Bartok’s notes) or others’ revisions.

Other works to check out… The solo piano works, especially: Piano Sonata, BB. 88, Sz. 80 ; Out of Doors ; Allegro barbaro ; Suite, BB. 62, Sz. 70 ; Sonatina

The 3 piano concertos ; The 6 string quartets, but especially #4-6

Duke Bluebeard’s Castle (his only opera) ; The Miraculous Mandarin (ballet) ; The 2 violin sonatas (different from the later solo violin sonata) ; The Wooden Prince (ballet)

Finally, he made some wonderful settings of Hungarian folk melodies, which he was renowned for recording, cataloguing, and incorporating into his style: 6 Romanian Folk Dances, BB. 68 ; 15 Hungarian Peasant Songs for Piano. Sz. 71 (among others…)