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Virtual reality (VR) is one of the emerging technologies in recent years. It brings a sense of real world experience in simulated environments, hence, it is being used in many applications for example in live sporting events, music recordings and in many other interactive multimedia applications. VR makes use of multimedia content, and videos are a major part of it. VR videos are captured from multiple directions to cover the entire 360 field-of-view. It usually employs, multiple cameras of wide field-of-view such as fisheye lenses and the camera arrangement can also vary from linear to spherical set-ups. Videos in VR system are also subjected to constraints such as, variations in network bandwidth, heterogeneous mobile devices with limited decoding capacity, adaptivity for view switching in the display. The uncompressed videos from multiview cameras are redundant and impractical for storage and transmission. The existing video coding standards compresses the multiview videos effi ciently. However, VR systems place certain limitations on the video and camera arrangements, such as, it assumes rectilinear properties for video, translational motion model for prediction and the camera set-up to be linearly arranged. The aim of the thesis is to propose coding schemes which are compliant to the current video coding standards of H.264/AVC and its successor H.265/HEVC, the current state-of-the-art and multiview/scalable extensions. This thesis presents methods that compress the multiview videos which are captured from eight cameras that are arranged spherically, pointing radially outwards. The cameras produce circular fi sheye videos of 195 degree field-of-view. The final goal is to present methods, which optimize the bitrate in both storage and transmission of videos for the VR system. The presented methods can be categorized into two groups: optimizing storage bitrate and optimizing streaming bitrate of multiview videos. In the storage bitrate category, six methods were experimented. The presented methods competed against simulcast coding of individual views. The coding schemes were experimented with two data sets of 8 views each. The method of scalable coding with inter-layer prediction in all frames outperformed simulcast coding with approximately 7.9%. In the case of optimizing streaming birates, five methods were experimented. The method of scalable plus multiview skip-coding outperformed the simulcast method of coding by 36% on average. Future work will focus on pre-processing the fi sheye videos to rectilinear videos, in-order to fit them to the current translational model of the video coding standards. Moreover, the methods will be tested in comprehensive applications and system requirements.