In recent years, Internet traffic patterns have been changing. Most of the traffic demand by end users is multimedia, in particular, video streaming accounts for over 53%. This demand has led to improved network infrastructures and computing architectures to meet the challenges of delivering these multimedia services while maintaining an adequate quality of experience. Focusing on the preparation and adequacy of multimedia content for broadcasting, Cloud and Edge Computing infrastructures have been and will be crucial to offer high and ultra-high definition multimedia content in live, real-time, or video-on-demand scenarios. For these reasons, this review paper presents a detailed study of research papers related to encoding and transcoding techniques in cloud computing environments. It begins by discussing the evolution of streaming and the importance of the encoding process, with a focus on the latest streaming methods and codecs. Then, it examines the role of cloud systems in multimedia environments and provides details on the cloud infrastructure for media scenarios. After doing a systematic literature review, we have been able to find 49 valid papers that meet the requirements specified in the research questions. Each paper has been analyzed and classified according to several criteria, besides to inspect their relevance. To conclude this review, we have identified and elaborated on several challenges and open research issues associated with the development of video codecs optimized for diverse factors within both cloud and edge architectures. Additionally, we have discussed emerging challenges in designing new cloud/edge architectures aimed at more efficient delivery of media traffic. This involves investigating ways to improve the overall performance, reliability, and resource utilization of architectures that support the transmission of multimedia content over both cloud and edge computing environments ensuring a good quality of experience for the final user.