Longitudinal studies of microbial communities have emphasized that host-associated microbiota are highly dynamic as well as underscoring the potential biomedical relevance of understanding these dynamics. Despite this increasing appreciation, statistical challenges in the design and analysis of longitudinal microbiome studies such as sequence counting, technical variation, signal aliasing, contamination, sparsity, missing data, and algorithmic scalability remain. In this review we discuss these challenges and highlight current progress in the field. Where possible, we try to provide guidelines for best practices as well as discuss how to tailor design and analysis to the hypothesis and ecosystem under study. Overall, this review is intended to serve as an introduction to longitudinal microbiome studies for both statisticians new to the microbiome field as well as biologists with little prior experience with longitudinal study design and analysis.