The confluence of 5G and AI is transforming wireless networks to deliver diverse services at the edge, driving toward a vision of pervasive distributed intelligence. Future 6G networks will need to deliver quality of experience through seamless integration of communication, computation, and AI. Therefore, networks must become intelligent, distributed, scalable, and programmable platforms across the continuum of data delivery to address the ever increasing service requirements and deployment complexity. We present novel results across three research directions that are expected to be integral to 6G systems, and also discuss newer 6G metrics.