Phytanic acid (PA) (3,7,11,15-tetramethylhexadecanoic acid) is a methyl-branched fatty acid that enters the body through food consumption, primarily through red meat, dairy products, and fatty marine foods. The metabolic byproduct of phytol is PA, which is then oxidized by the ruminal microbiota and some marine species. The first methyl group at the 3-position prevents the β-oxidation of branched-chain fatty acid (BCFA). Instead, α-oxidation of PA results in the production of pristanic acid (2,10,14-tetramethylpentadecanoic acid) with CO2. This fatty acid (FA) builds up in individuals with certain peroxisomal disorders and is historically linked to neurological impairment. It also causes oxidative stress in synaptosomes, as demonstrated by an increase in the production of reactive oxygen species (ROS), which is a sign of oxidative stress. This review concludes that the nutraceuticals (melatonin, piperine, quercetin, curcumin, resveratrol, epigallocatechin-3-gallate (EGCG), coenzyme Q10, ω-3 FA) can reduce oxidative stress and enhanced the activity of mitochondria. Furthermore, the use of nutraceuticals completely reversed the neurotoxic effects of PA on NO level and membrane potential. Additionally, the review further emphasizes the urgent need for more research into dairy-derived BCFAs and their impact on human health.