Over billions of years, nature has developed effective and sustainable systems that can serve as inspiration for creative solutions to contemporary issues. Since long time, designers, engineers, researchers, and artists have drawn inspiration from environment. Scientists have developed a number of intelligent computer paradigms inspired by nature, which are based on natural processes. These paradigms have demonstrated adaptable and successful solutions to real-world and challenging issues throughout the past few decades. Several heuristic algorithms, sometimes referred to as nature-inspired algorithms, have been developed for stochastic optimization problems. As a result of their adaptability and efficiency, nature-inspired algorithms are currently popular. Practically challenging problems have been successfully solved by nature-inspired intelligent computing paradigms because of their parallelism, derivative-free nature, and ease of scaling. Nonetheless, there are a few major problems with swarm intelligence and nature-inspired computing. In-depth reviews of certain current nature-inspired algorithms are given in this chapter, with a focus on their mathematical underpinnings and search processes. Additionally, this chapter provides a thorough algorithmic foundation for minimizing inappropriate metaphors by demonstrating the relationship between these paradigms and natural systems as well as their practical implementations. The optimization of algorithms and the usage of these methods in engineering and the medical field are the primary focus of this chapter. Nature-inspired computing replicates natural phenomena and biological processes to create effective problem-solving algorithms. Nature-inspired computing aids disease diagnosis, treatment, and monitoring of patients in healthcare. Nature-inspired computing has the potential of expanding even further, closing gaps between artificial intelligence and real-life problem solving.