Until recently, the measure of microbial diversity has been limited by our technological tools for detecting and distinguishing different kinds of microorganisms. With the advent of affordable large-scale sequencing of environmental DNA, our ability to measure microbial diversity may be limited now by our mathematical tools for modeling the nature of microbial diversity. I will discuss three basic problems of measuring microbial diversity: 1) Constraining the apparent near-infinite richness of microbial species. 2) Assembling random environmental DNA sequences into coherent genomes (i.e. metagenomics). 3) Building models of ecological interactions by integrating DNA sequence data with environmental data. I will highlight each problem with examples from my research on subsurface, hydrogen-fueled microbial ecosystems.