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 powerful simulation methods. In recent years, we
have developed powerful Monte Carlo algorithms for hard disks and
related systems. I will in particular show how the event-chain Monte
Carlo algorithm has allowed us to prove 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 finally describe how a
new factorized Metropolis filter transforms the event-chain algorithm
into a paradigm for general Monte Carlo calculations. First results
with the generalized algorithm have allowed us to establish the phase
diagram for two-dimensional soft disks and Yukawa particles.