This paper provides a survey of projection-based model reduction methods for parametric dynamical systems. The goal is to generate low-cost but accurate models that characterize system response for different values of parameters. The paper discusses various methods for parametric model reduction, including rational interpolation, balanced truncation, proper orthogonal decomposition, and greedy algorithms. It also covers the construction of parameterized reduced models and discusses the advantages and disadvantages of different approaches. The paper highlights the importance of parametric model reduction in design, control, optimization, and uncertainty quantification, where repeated model evaluations over different parameter values are required. The paper also discusses error measures for assessing the quality of reduced models, including time-domain and frequency-domain error measures. The paper concludes with an outlook on future research directions in parametric model reduction.This paper provides a survey of projection-based model reduction methods for parametric dynamical systems. The goal is to generate low-cost but accurate models that characterize system response for different values of parameters. The paper discusses various methods for parametric model reduction, including rational interpolation, balanced truncation, proper orthogonal decomposition, and greedy algorithms. It also covers the construction of parameterized reduced models and discusses the advantages and disadvantages of different approaches. The paper highlights the importance of parametric model reduction in design, control, optimization, and uncertainty quantification, where repeated model evaluations over different parameter values are required. The paper also discusses error measures for assessing the quality of reduced models, including time-domain and frequency-domain error measures. The paper concludes with an outlook on future research directions in parametric model reduction.