Longitudinal microbiome studies are used to capture the temporal variation within the microbiome to gain mechanistic insights into microbial systems. However, longitudinal microbiome data produced by both 16S rRNA gene sequencing and metagenomic shotgun sequencing have many analytical challenges, due to the nature of the microbiome data in addition to standard longitudinal data. We have categorised statistical methods for these longitudinal data according to their analytical objectives- (1) to identify differentially expressed microorganisms; (2) to identify microorganisms evolving concomitantly across time; and (3) to identify biotic interactions. We compared existing methods on both simulation and real 16S data to highlight the most performant methods, and we discuss the challenges ahead for these increasingly popular studies.