Today, there is a marked increase in interest in the share of renewable energy sources in the energy mix, which benefits the environment. This also applies to the energy of sea (wave) current, as, without a doubt, the offshore area is becoming one of the leading areas of renewable energy, which translates into changes in energy production. This can be exemplified by the latest research in the context of theory, design, modeling, as well as application, control, and monitoring of wave turbines to enhance their performance. This article reviews the research in this context, systematizes information, identifies literature gaps, and presents future directions in this area. For this purpose, 3240 English-language publications from 2015 to 2024 were identified in the Scopus database. The data are analyzed according to the selected research domains. Some of them are review or conceptual in nature, while others are empirical in nature (experimental attempts and case studies). From this point of view, it becomes possible not only to systematize the state-of-the-art but also to identify future research prospects.