Here are some excerpts from his obituary by Randy Kennedy in the New York Times:
Twombly's childlike scribbles and poetic engagement with antiquity left him stubbornly out of step with the movements of postwar American art even as he became one of the era's most important painters.
He once practiced drawing in the dark to make his lines less purposeful, steadfastly follow[ing] his own program...
Twombly said "I have my pace and way of living and I'm not looking for something." Of reputation and artistic acclaim, he added: "It's something I don't think about. If it happens, it happens, but don't bother me with it. I couldn't care less."
Of Twombly's work, Roberta Smith wrote, "Few 20th-century artists corroborated as insistently Schiller's assertion that 'all art is dedicated to joy.'
Cy Twombly, in front of his work