Open RAN is an emerging vision and an advancement of the Radio Access Network (RAN). Its purpose is to implement a vendor and network-generation agnostic RAN, provide networking solutions across all service requests, and implement artificial intelligence solutions in different stages of an end-to-end communication path. The 5th Generation (5G) and beyond the 5th Generation (B5G) of networking introduce and support new use cases, such as tactile internet and autonomous driving. The complexity and innovative nature of these use cases require continuous innovation at a high pace in the RAN. The traditional approach of building end-to-end RAN solutions by only one vendor hampers the speed of innovation-furthermore, the lack of a standard approach to implementing artificial intelligence complicates the compatibility of products with the RAN ecosystem. O-RAN Alliance, a community of industry and academic experts in RAN, works on writing Open RAN specifications on top of the 3rd Generation Partnership Project (3GPP) standards. Founded on these specifications, the aim of this paper is to introduce open research topics in Open RAN that overlap the interests of both AI and telecommunication researchers. The paper provides an overview of the architecture and components of Open RAN, then explores AI use cases in Open RAN. Also, this survey includes some plausible AI deployment scenarios that the specifications have not covered. Open RAN in future cities creates opportunities for various use cases across different sectors, including engineering, operations, and research that this paper addresses.