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A fundamental challenge in today's arena of complex systems is the design and development of accurate and robust signal processing methods. These methods should be capable to adapt quickly to unexpected changes in the data and operate under minimal model assumptions. Systems in Nature also do signal processing and often do it optimally. Therefore, it makes much sense to understand what Nature does and try to mimic it and do even better. In return, the results of better signal processing methods may lead to new advancements in science and technology and in understanding Nature. In this presentation methods for signal processing that borrow concepts and principles found in Nature are addressed including ant optimization, swarm intelligence and genetic algorithms. However, the emphasis of the presentation is on Monte Carlo-based methods, and in particular, methods related to particle filtering, cost-reference particle filtering, and population Monte Carlo. In the past decade and a half, Monte Carlo-based methods have gained considerable popularity in dealing with nonlinear and/or non-Gaussian systems. The three groups of methods share the feature that they explore spaces of unknowns using particles and weights (costs) assigned to the particles. In most versions of these methods, particles move independently and in accordance with the dynamics of the assumed model of the states. Interactions among particles only occur through the process of resampling rather than through local interactions as is common in physical and biological systems. Such interactions can improve the performance of the methods and can allow for coping with more challenging problems with better efficiency and accuracy. We show how we apply these methods to problems in engineering, economics, and biology.