The challenge of finding a global optimum in a solution search space with limited resources and higher accuracy has given rise to several optimization algorithms. Generally, the gradient-based optimizers converge to the global solution very accurately, but they often require a large number of iterations to find the solution. Researchers took inspiration from different natural phenomena and behaviours of many living organisms to develop algorithms that can solve optimization problems much quicker with high accuracy. These algorithms are called nature-inspired meta-heuristic optimization algorithms. These can be used for denoising signals, updating weights in a deep neural network, and many other cases. In the state-of-the-art, there are no systematic reviews available that have discussed the applications of nature-inspired algorithms on biomedical signal processing. The paper solves that gap by discussing the applications of such algorithms in biomedical signal processing and also provides an updated survey of the application of these algorithms in biomedical image processing. The paper reviews 28 latest peer-reviewed relevant articles and 26 nature-inspired algorithms and segregates them into thoroughly explored, lesser explored and unexplored categories intending to help readers understand the reliability and exploration stage of each of these algorithms.