How can agile and traditional waterfall development methodologies co-exist?

Over the course of my career, I’ve seen such a shift in approaches to how we develop applications. I was raised in the traditional waterfall method, like many of us. Then I experienced the agile method and saw its benefits as well as limitations. Today, as a CIO overseeing large teams and diverse organizational needs, I see the need for both methods to co-exist and to cross-pollinate. But can they co-exist when they are so different? I’d love to hear your experiences.