As a classic topic in bioinformatics, the fragment assembly problem has been studied for over two decades. Fragment assembly algorithms take a set of DNA fragments as input, piece them together into a set of aligned overlapping fragments (i.e., contigs), and output a consensus sequence for each of the contigs. The rapid advance of massively parallel sequencing, often referred to as next-generation sequencing (NGS) technologies, has revolutionized DNA sequencing by reducing both its time and cost by several orders of magnitude in the past few years, but posed new challenges for fragment assembly. As a result, many new approaches have been developed to assemble NGS sequences, which are typically shorter with a higher error rate, but at a much higher throughput, than classic methods provided. In this chapter, we review both classic and new algorithms for fragment assembly, with a focus on NGS sequences. We also discuss a few new assembly problems emerging from the broader applications of NGS techniques, which are distinct from the classic fragment assembly problem.