Monte Carlo is an exceptionally powerful numerical integration technique. It offers relatively straightforward, indeed sometimes deceptively simple, algorithms for solving some of the most complex, real-world problems. One of the most widely used implementations of the Monte Carlo technique is to solve the Boltzmann transport equation describing the passage of particles (radiation) through media. In this talk, I will present an overview of Monte Carlo radiation transport and its applications, which range from high-energy astrophysics to medical physics. I will also discuss two of the most sophisticated Monte Carlo radiation transport codes currently available and compare their advantages and limitations. Finally, I will discuss the future challenges that lay ahead for Monte Carlo radiation transport modelling of radiobiological effects on DNA scales. http://www.maths.usyd.edu.au/u/AppliedSeminar/abstracts/2008/kuncic.html