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The fitness landscape encodes the mapping of genotypes to fitness and provides a succinct representation of possible trajectories followed by an evolving population. Evolutionary accessibility is quantified by the existence of fitness-monotonic paths connecting far away genotypes. Studies of accessibility percolation use probabilistic fitness landscape models to explore the emergence of such paths as a function of the initial fitness, the parameters of the landscape or the structure of the genotype graph. This chapter reviews these studies and discusses their implications for the predictability of evolutionary processes.