As the size and distance from shore of new offshore wind power plants (OWPPs) increase, connection to shore using high-voltage (HV) direct-current (DC) technology becomes more cost-effective. Currently, every offshore wind power plant has a collection system based on medium-voltage alternating-current technology. Such systems rely on heavy and bulky low-frequency (i.e., 50 or 60 Hz) transformers: a drawback offshore, where equipment weight and space are restricted. Consequently, there is growing interest in medium-voltage direct-current collection systems, in which low-frequency transformers are replaced with DC/DC converters equipped with lighter and smaller medium-frequency transformers. However, the deployment of all-DC OWPPs still faces several challenges. Based on a very comprehensive and critical literature review, three of them are identified and discussed in this paper. The first challenge is the technological gap at component level. In this work, the DC/DC converter topologies most suitable for application to OWPPs are described and compared. The second challenge is the controllability of DC collection systems. Parallel, series and hybrid DC collection system layouts are presented and discussed. The third challenge is the compliance of all-DC OWPPs with current requirements for their connection to the onshore grids. The three challenges are discussed to highlight current research gaps and potential future directions.