Research in origins of life is an intrinsically multidisciplinary field, aimed at finding answers to the formidably complex problem of understanding the emergence of life from the modern versions of Charles Darwin's celebrated "primordial soup". In the last few years, thanks to the increasing computational power and the development of sophisticated theoretical and numerical methods, several computational chemistry and physics groups have invested this field, providing new microscopic insights on fundamental prebiotic chemistry phenomena possibly occurring in the early Earth and outer space. This review presents the most successful and powerful approaches in computational chemistry, and the main results thus obtained in prebiotic chemistry and origins of life. The aim of this work is both to describe the state-of-the-art in computational prebiotic chemistry, possibly useful both to theorists and experimentalists in origins of life research, and to suggest future directions and new perspectives offered by modern simulation tools.