[3] In 2004, Joan Acocella called Cornejo "the most technically accomplished male ballet dancer in the United States.

Major roles have been created on him by Alexei Ratmansky,[10][11] Mauro Bigonzetti,[12] Trey McIntyre,[4] Jorma Elo,[5] Twyla Tharp,[12] and Martha Clarke,[7] among others.

[14] In 2015, Cornejo was the artistic director of the Latin American Stars Gala, part of the Performing Arts Center of Los Angeles County's 50th anniversary celebrations.

[15][16] In 2014, Cornejo was awarded the Prix Benois de la Danse for Outstanding Male Dancer, for his portrayals of Aminta in Sylvia, Caliban in The Tempest and a leading role in Symphony #9, as well as for his appearance in Martha Clarke’s Chéri.

[2] In 2014, he won the "Best Male Dancer" award of the international Prix Benois de la Danse,[3][20] along with the Positano Prize in Italy.

"[21] The NYT's chief dance critic, Alastair Macaulay, praised his artistic range in 2016: "His jumps' height and his turns' speed matter less than their windblown, tilting ecstasy and shining, boyish fervor.

"[22] In the Los Angeles Times in 2013, Susan Reiter wrote: "Cornejo has elegantly and boldly left expectations behind.

"[6] Critic Gia Kourlas called "Momentum", a piece Cornejo choreographed to music by Philip Glass, an "unpretentious exploration of his clean virtuosity.

[4][5][23] Cornejo has remarked that he feels "much bigger" than others perceive him, enjoying "big, slow" adagio choreography as well as the quicker movements generally assigned to smaller dancers.