Bioactive compounds in food can have high impacts on human health, such as antioxidant, antithrombotic, antitumor, and anti-inflammatory activities. However, many of them are sensitive to thermal treatments incurred during processing, which can reduce their availability and activity. Milk, including ovine, caprine, bovine, and human is a rich source of bioactive compounds, including immunoglobulins, vitamins, and amino acids. However, processing by various novel thermal and non-thermal technologies has different levels of impacts on these compounds, according to the studies reported in the literature, predominantly in the last 10 years. The reported effect of these technologies either covers microbial inactivation or the bioactive composition; however, there is a lack of comprehensive compilation of studies that compare the effect of these technologies on bioactive compounds in milk (especially, caprine and ovine) to microbial inactivation at similar settings. This research gap makes it challenging to conclude on the specific processing parameters that could be optimized to achieve targets of microbial safety and nutritional quality at the same time. This review covers the effect of a wide range of thermal and non-thermal processing technologies including high-pressure processing, pressure-assisted thermal sterilization, pulsed-electric field treatment, cold plasma, microwave-assisted thermal sterilization, ultra-high-pressure homogenization, ultrasonication, irradiation on the bioactive compounds as well as on microbial inactivation in milk. Although a combination of more than one technology could improve the reduction of bacterial contaminants to meet the required food safety standards and retain bioactive compounds, there is still scope for research on these hurdle approaches to simultaneously achieve food safety and bioactivity targets.