Research and innovation are highlighted as significant priorities among Higher Education Institutions (HEIs) in the Philippines. However, most HEIs in the country have a poor culture of research and innovation, which results in low academic productivity. This literature review was conducted to understand the dynamics of a teaching, research, and innovative university, discuss the current status of Philippine HEIs in terms of research (R&D)-innovation productivity, and excerpt best practices from leading universities in the country as a benchmark for other higher institutions toward building a culture of research and innovation. This study highlights different viewpoints but reveals one thing in common among the established research universities: they have exemplary administrative leadership and proper institutional framework, with strong qualifications from their faculty to absorb all the resources pouring in, thereby significantly boosting them and yielding a fruitful result in terms of research and innovation. With these, other Philippines HEIs need to build and develop a vital research and innovative culture among their stakeholders to produce tangible outcomes, which can be utilized for industry-related improvements and new market opportunities, and to address the nation's most pressing issues. Without the support and proper compensation within academia, industry, and government, the pool of talents will be put on the shelf. Nevertheless, leveling up from teaching institutions to become a research and innovative academia remains interesting as it depends primarily on the university's vision and actions, which are mostly affected by its internal and external environment. This paper hopes to be a springboard in formulating policy and practice toward enhancing research and innovation efficiency among the Philippine HEI's that could contribute to the overall nationwide progress.