This paper aims to examine the influence of various catalysts on biodiesel production, especially from non-food feedstocks with an ambition to optimize the catalytic biodiesel production. Homogenous acid catalysts are mainly used in biodiesel production, but they cannot be recovered and demand costly fuel purification as being corrosive. Similarly, enzyme catalysts are expensive in industrial-scale production of biodiesel. However, heterogeneous catalysts simplify the easy separation of product and by-products from the catalyst along with catalyst reusability and reduction of waste. Solid acid and base catalysts offer more advantages due to their non-toxicity, high surface area, reusability, higher stability and the simplicity of purification. Heterogeneous base catalysts yield better activity than heterogeneous acid catalysts, however, they cannot esterify large amounts of free fatty acids (FFAs) in non-food feedstocks. The solid acid catalysts have the added advantages of being more tolerant to high amounts of FFAs and being able to simultaneously esterify FFAs and transesterify triglycerides in cheap feedstocks like waste cooking oil. Recently, an array of inorganic, organic and polymeric solid acid and nanomaterial-based catalysts have been developed using cheap feedstock. However, the issues of low reactivity, small pore sizes, low stabilities, long reaction times, and high reaction temperatures still need to be solved. These developments of producing efficient, cheap, durable, and stable solid acid and nanomaterial-based catalysts have been critically reviewed in this study. Furthermore, the challenges and future perspectives of production of biodiesel and its industry growth have also been discussed.