  The paper surveys the evolution of main algorithmic techniques to compare and
search biological sequences. We highlight key algorithmic ideas emerged in
response to several interconnected factors: shifts of biological analytical
paradigm, advent of new sequencing technologies, and a substantial increase in
size of the available data. We discuss the expansion of alignment-free
techniques coming to replace alignment-based algorithms in large-scale
analyses. We further emphasize recently emerged and growing applications of
sketching methods which support comparison of massive datasets, such as
metagenomics samples. Finally, we focus on the transition to population
genomics and outline associated algorithmic challenges.
