This chapter introduces the motivation and background for Sequential Monte Carlo (SMC) methods. It highlights that many real-world data analysis tasks involve estimating unknown quantities from sequential observations, often requiring online inference. While linear Gaussian state-space models and hidden Markov models (HMMs) admit exact analytical solutions, real-world data often exhibit non-Gaussianity, high dimensionality, and nonlinearity, making these models inadequate. SMC methods provide a flexible, easy-to-implement, and parallelizable approach to computing posterior distributions, especially in complex and high-dimensional settings. The chapter also notes the recent proliferation of SMC methods and their applications across various fields, such as financial modeling, target tracking, computer vision, and machine learning. The book is structured into three parts: theoretical foundations, efficiency improvements, and practical applications, with each part covering a wide range of topics and authors.This chapter introduces the motivation and background for Sequential Monte Carlo (SMC) methods. It highlights that many real-world data analysis tasks involve estimating unknown quantities from sequential observations, often requiring online inference. While linear Gaussian state-space models and hidden Markov models (HMMs) admit exact analytical solutions, real-world data often exhibit non-Gaussianity, high dimensionality, and nonlinearity, making these models inadequate. SMC methods provide a flexible, easy-to-implement, and parallelizable approach to computing posterior distributions, especially in complex and high-dimensional settings. The chapter also notes the recent proliferation of SMC methods and their applications across various fields, such as financial modeling, target tracking, computer vision, and machine learning. The book is structured into three parts: theoretical foundations, efficiency improvements, and practical applications, with each part covering a wide range of topics and authors.