Large-scale genomics demands computational methods that scale sublinearly with the growth of data. We review several data structures and sketching techniques that have been used in genomic analysis methods. Specifically, we focus on four key ideas that take different approaches to achieve sublinear space usage and processing time: compressed full text indices, approximate membership query data structures, locality-sensitive hashing, and minimizers schemes. We describe these techniques at a high level and give several representative applications of each.