Currently, a huge amount of data is available across various domains including biological data. Classification of these data, clustering, and data analysis is tedious and has become popular in recent research. In particular, bio-inspired computing is the field that mends together mathematics, computer science, and biology to develop tools to store, scrutinize, and interpret the biological data. It is also used to solve real life problems like sequencing biological data, data clustering, and optimization. Swarm intelligence is an emerging field of biologically inspired artificial intelligence technique that is based on the behavioral models of social insects. This chapter provides an overview of swarm intelligence algorithms in solving bio-inspired computing problems. It is an attempt to explore the working nature, applications, and generative power of various bio-inspired computing algorithms. The main intent is to furnish a comprehensive study of swarm intelligence algorithms in the literature so as to inspire further research in the area of biologically inspired computing.