Genome assembly is a core task in the field of genomics. The availability of long-read sequencing technologies enabled the construction of high-quality complex genomes, including phasing of heterozygous contigs. This chapter provides an overview of the main algorithmic techniques for genome assembly. It starts revisiting the two main data structures used for unphased genome assembly, namely, the overlap graph and the de Bruijn graph. Then, it describes current protocols and sequencing alternatives such as trio data and Hi-C to provide long-range information for scaffolding and phasing. Next, it describes the metrics that have been developed to evaluate completeness accuracy and base pair quality. Finally, this chapter provides detailed information on the core algorithmic ideas of four different tools to perform phased genome assemblies (FALCON, HiCanu, Hifiasm, and NGSEP). A review of classic techniques for phasing based on aligned reads is included to provide a context of basic concepts needed to understand the algorithms implemented in the genome assemblers.