To keep supporting next-generation requirements, the radio access infrastructure will increasingly densify. Cell-free (CF) network architectures are emerging, combining dense deployments with extreme flexibility in allocating resources to users. In parallel, the Open Radio Access Networks (O-RAN) paradigm is transforming RAN towards an open, intelligent, virtualized, and fully interoperable architecture. This paradigm brings the needed flexibility and intelligent control opportunities for CF networking. In this paper, we document the current O-RAN terminology and contrast it with some common CF processing approaches. We then discuss the main O-RAN innovations and research challenges that remain to be solved.