In this chapter, various parameter estimation methods are presented. First, the Markov chain Monte Carlo (MCMC) technique is introduced, which is then applied to estimate model parameters utilizing the Metropolis-Hastings algorithm. Next, linear regression and the maximum likelihood estimation are discussed, followed by the expectation-maximization (EM) algorithm is described, aiming to estimate model parameters with partial observations. The EM algorithm alternates between estimating the parameters via maximum likelihood estimation and recovering the unobserved state with uncertainty quantification via nonlinear smoothing. Closed analytic formulae are available for this entire parameter estimation procedure when the EM is applied to the CGNS developed in Chap. 8, where physics constraints are naturally incorporated. This chapter also discusses some theoretical and numerical results of parameter estimation via data assimilation, which treats parameters as augmented state variables. Finally, learning the structure and parameters of complex dynamical systems utilizing data is discussed. In addition to the constrained optimization via an L1 regularization, the sparse identification of the model structure can also be carried out in light of information theory. The latter exploits causation entropy to determine the model structure with a physical justification, which also significantly facilitates the parameter estimation that becomes a simple quadratic optimization problem.