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We present updates to the problems on Hirzebruch's 1954 problem listfocussing on open problems, and on those where substantial progress has beenmade in recent years. We discuss some purely topological problems, as well asgeometric problems about (almost) complex structures, both algebraic andnon-algebraic, about contact structures, and about (complementary pairs of)foliations.

Updates on Hirzebruch's 1954 Problem List