AbstractWe study a new geometric bootstrap percolation model, line percolation, on the d‐dimensional integer grid . In line percolation with infection parameter r, infection spreads from a subset of initially infected lattice points as follows: if there exists an axis‐parallel line L with r or more infected lattice points on it, then every lattice point of on L gets infected, and we repeat this until the infection can no longer spread. The elements of the set A are usually chosen independently, with some density p, and the main question is to determine , the density at which percolation (infection of the entire grid) becomes likely. In this paper, we determine up to a multiplicative factor of and up to a multiplicative constant as for every fixed . We also determine the size of the minimal percolating sets in all dimensions and for all values of the infection parameter.