Traditional ITU-T fixed frequency grid-based optical transport networks suffer several drawbacks such as low fiber spectral efficiency, difficulty in supporting large-bandwidth super-channels, and inflexibility in network bandwidth reconfiguration and modification. To overcome these drawbacks, a new-generation optical transport network based on the concepts of agile spectrum operation and elastic bandwidth allocation has been recently proposed and is receiving increasing attention. This new-generation network is called coherent optical orthogonal frequency-division multiplexing (CO-OFDM) optical transport network. It employs the promising CO-OFDM transmission technique and the new-generation bandwidth-variable ROADMs that use the coherent detection capability of the CO-OFDM transmission for optical channel filtering. The CO-OFDM optical transport network is characterized by arbitrarily assigning center frequency and bandwidth of an optical channel, thereby providing flexibility in network design and operation and achieving efficient fiber spectrum utilization. Despite the increasing attention and considerable progress, there are still many outstanding issues regarding the implementation of CO-OFDM optical transport networks. This article reviews the literature on the architectures of the CO-OFDM optical transport network and discusses key issues, particularly involving network control plane, lightpath routing and spectrum assignment, impact of channel modulation format and optical reach, subwavelength traffic grooming, network survivability, and network reconfiguration.