Following his win over Andy Murray in the first round, Kyrgios against prevailed in three sets against fellow Brit Edmund, coming through 7-6 (7-3) 6-7 (5-7) 6-3.
Kyrgios will face 2017 winner Feliciano Lopez or Milos Raonic in the quarter-finals.
Cilic stuns Djokovic to claim Queen’s Club title
More to follow.
Relentless Cilic edges Kyrgios to set up Djokovic final
Murray loses to Kyrgios on return