Firm growth is a central topic in entrepreneurship research. The approach taken here is to survey the literature on lumps and discontinuities in the growth process, which may well correspond to the most interesting cases of firm growth. Our interdisciplinary review investigates stages of growth models, growth modes, growth strategies, and barriers and thresholds that hinder the growth of firms. Firm growth is theorized to be characterized by the addition and reconfiguration of lumpy discrete resources. The distribution of annual growth rates follows a heavy-tailed distribution, which has led to interest in growth paths, growth spells, growth spikes, and the phenomenon of High-Growth Firms (HGFs). We conclude with implications for empirical and theoretical research.