Reconstructing historical variation of population size from sequence and single-nucleotide polymorphism (SNP) data is valuable for understanding the evolutionary history of species. Changes in the population size of humans have been thoroughly investigated, and we review different methodologies of demographic reconstruction, specifically focusing on human bottlenecks. In addition to the classical approaches based on the site-frequency spectrum (SFS) or based on linkage disequilibrium, we also review more recent approaches that utilize atypical shared genomic fragments, such as identical by descent or homozygous segments between or within individuals. Compared with methods based on the SFS, these methods are well suited for detecting recent bottlenecks. In general, all these various methods suffer from bias and dependencies on confounding factors such as population structure or poor specification of the mutational and recombination processes, which can affect the demographic reconstruction. With the exception of SFS-based methods, the effects of confounding factors on the inference methods remain poorly investigated. We conclude that an important step when investigating population size changes rests on validating the demographic model by investigating to what extent the fitted demographic model can reproduce the main features of the polymorphism data.