Oxygen is one of the essential requirements for cell survival, retention, and proliferation. The field of regenerative medicine and tissue engineering (TE) has realized considerable achievements for the regeneration of tissues. However, tissue regeneration still lacks the full functionality of solid organ implantations; limited cell survival and retention due to oxidative stress and hypoxia in the deeper parts of tissues remains a perpetual challenge. Especially prior to neovascularization, hypoxia is a major limiting factor, since oxygen delivery becomes crucial for cell survival throughout the tissue-engineered construct. Oxygen diffusion is generally limited in the range 100–200 μm of the thickness of a scaffold, and the cells located beyond this distance face oxygen deprivation, which ultimately leads to hypoxia. Furthermore, before achieving functional anastomosis, implanted tissues will be depleted of oxygen, resulting in hypoxia (<5% dissolved oxygen) followed by anoxic (<0.5% dissolved oxygen) microenvironments. Different types of approaches have been adopted to establish a sustained oxygen supply both in vitro and in vivo. In this review, we have summarized the recent developments in oxygen-generating and/or releasing biomaterials for enhancing cell survival in vitro, as well as for promoting soft and hard tissue repair, including skin, heart, nerve, pancreas, muscle, and bone tissues in vivo. In addition, redox-scavenging biomaterials and oxygenated scaffolds have also been highlighted. The surveyed results have shown significant promise in oxygen-producing biomaterials and oxygen carriers for enhancing cell functionality for regenerative medicine and TE applications. Taken together, this review provides a detailed overview of newer approaches and technologies for oxygen production, as well as their applications for bio-related disciplines.