The hard-disk model has exerted outstanding influence on computational physics and statistical mechanics.  Decades ago, hard disks were the first system to be studied by Markov-chain Monte Carlo methods and by molecular dynamics.  It was in hard disks, through numerical simulations, that a two-dimensional melting transition was first seen to occur even though such systems cannot develop long-range crystalline order.  Analysis of the system was made difficult by the absence of adequate simulation methods.
In recent years, we  have developed a number of powerful Monte Carlo algorithms for hard disks and related systems. I will in particular show how  the powerful event-chain Monte Carlo algorithm has allowed us to
show that hard disks melt  with a first-order transition from the liquid to the hexatic and a continuous transition from the hexatic to the solid. I will finish with discussions on the general theory of two-dimensional melting and on the generalizations of the event-chain algorithm.