Chern's contribution to the Hopf problem: An exposition based on Bryant's paper

We give a comprehensive account of Chern's Theorem that S^6 admits no omega-compatible almost complex structures. No claim to originality is being made, as the paper is mostly an expanded version of material already in the literature. This article extends the talks that both authors gave in Marburg during the conference "(Non)existence of complex structures on S^6" in April 2017.
Misprints corrected