The year 2001 marked the 50th anniversary of the discovery of the Phillips chromium catalyst, from which today's worldwide high‐density polyethylene industry sprang. Appropriately, during that year the discoverers of this catalyst system, J. Paul Hogan and Robert L. Banks, were inducted into the National Inventors Hall of Fame, in Akron, OH, to join other distinguished inventors spanning two centuries who have shaped our world. This chapter reviews our understanding of the chemistry associated with that catalyst system, which is used globally to produce perhaps half of the world's high‐density polyethylene, and it provides examples of how that chemistry is exploited commercially.