The next-generation sequencing (NGS) revolution has drastically reduced time and cost requirements for sequencing of large genomes, and also qualitatively changed the problem of assembly. This article reviews the state of the art in de novo genome assembly, paying particular attention to mammalian-sized genomes. The strengths and weaknesses of the main sequencing platforms are highlighted, leading to a discussion of assembly and the new challenges associated with NGS data. Current approaches to assembly are outlined and the various software packages available are introduced and compared. The question of whether quality assemblies can be produced using short-read NGS data alone, or whether it must be combined with more expensive sequencing techniques, is considered. Prospects for future assemblers and tests of assembly performance are also discussed.