Open Radio Access Network (O-RAN) alliance was recently launched to devise a new RAN architecture featuring open, softwaredriven, virtual, and intelligent radio access architecture. O-RAN architecture is based on (1) disaggregated RAN functions that run as Virtual Network Function (VNF) and Physical Network Function (PNF); (2) the notion of RAN controller that runs centrally RAN applications such as mobility management, users' scheduling, radio resources allocation, etc. The RAN controller is in charge of enforcing the application decisions by using open interfaces with the RAN functions. One important feature introduced by O-RAN is the heavy usage of Machine Learning (ML) techniques, particularly Deep Learning (DL), to foster innovation and ease the deployment of intelligent RAN applications that are able to fulfill the Quality of Service (QoS) requirements of the envisioned 5G and beyond network services. In this work, we first give an overview of the evolution of RAN architectures toward 5G and beyond, namely C-RAN, vRAN, and O-RAN. We also compare them based on various perspectives, such as edge support, virtualization, control and management, energy consumption, and AI support. Then, we review existing DL-based solutions addressing the RAN part. We also show how they can be integrated/mapped to the O-RAN architecture since these works were not initially adapted to the O-RAN architecture. In addition, we present two case studies for DL techniques deployment in O-RAN. Furthermore, we describe how the main steps of deployed DL models in O-RAN can be automated, to ensure stable performance of these models, introducing ML system operations (MLOps) concept in O-RAN. Finally, we identify key technical challenges, open issues, and future research directions related to the Artificial Intelligence (AI)-enabled O-RAN architecture.