Over the years, significant research efforts have been made to extract bioactive compounds by applying different methodologies for various applications. For instance, the use of bioactive compounds in several commercial sectors such as biomedical, pharmaceutical, cosmeceutical, nutraceutical and chemical industries, has promoted the need of the most suitable and standardized methods to extract these bioactive constituents in a sophisticated and cost-effective manner. In practice, several conventional extraction methods have numerous limitations, e.g., lower efficacy, high energy cost, low yield, etc., thus urges for new state-of-the-art extraction methodologies. Thus, the optimization along with the integration of efficient pretreatment strategies followed by traditional extraction and purification processes, have been the primary goal of current research and development studies. Among different sources, algal biome has been found as a promising and feasible source to extract a broader spectrum of bioactive compounds with point-of-care application potentialities. As evident from the literature, algal bio-products includes biofuels, lipids, polyunsaturated fatty acids, pigments, enzymes, polysaccharides, and proteins. The recovery of products from algal biomass is a matter of constant development and progress. This review covers recent advancements in the extraction methodologies such as enzyme-assisted extraction (EAE), supercritical-fluid extraction (SFE), microwave-assisted extraction (MAE) and pressurized-liquid extraction (PLF) along with their working mechanism for extracting bioactive compounds from algal-based sources to meet bio-economy challenges and opportunities. A particular focus has been given to design characteristics, performance evaluation, and point-of-care applications of different bioactive compounds of microalgae. The previous and recent studies on the anticancer, antibacterial, and antiviral potentialities of algal-based bioactive compounds have also been discussed with particular reference to the mechanism underlying the effects of these active constituents with the related pathways. Towards the end, the information is also given on the possible research gaps, future perspectives and concluding remarks.