Both simulation and optimization have diverse applications with many different techniques and algorithms. In optimization, there are many different techniques and algorithms, especially a huge number of nature-inspired algorithms in recent years. Though these nature-inspired algorithms can be effective in practice, there are not many rigorous methods for analyzing such algorithms. This work first outlines the main components of optimization process and the related challenges in optimization and simulation. Then, some fundamental ideas in nature-inspired algorithms are reviewed, and different perspectives of algorithm analysis are discussed. Some open problems are then presented so as to inspire further research in these important areas.