Conditional Random Fields (CRFs) are a probabilistic method for structured prediction, combining the ability of graphical models to compactly model multivariate data with the ability of classification methods to perform prediction using large sets of input features. CRFs have been widely applied in natural language processing, computer vision, and bioinformatics. This tutorial introduces CRFs, focusing on modeling, inference, and parameter estimation. It assumes no prior knowledge of graphical modeling and is intended for practitioners in various fields. CRFs model the conditional distribution $ p(\mathbf{y}|\mathbf{x}) $ directly, which is essential for classification. They are a way of combining the advantages of classification and graphical modeling, allowing for compact modeling of multivariate data and leveraging large input features. Unlike generative models, CRFs do not model the joint distribution $ p(\mathbf{y}, \mathbf{x}) $, but instead focus on the conditional distribution $ p(\mathbf{y}|\mathbf{x}) $, making them more suitable for classification tasks. CRFs can be viewed as a generalization of logistic regression and as a discriminative analog of hidden Markov models. They are particularly useful for modeling complex dependencies between output variables, such as in sequence modeling, where the output variables are arranged in a sequence. Linear-chain CRFs are a special case where the output variables form a linear chain, while general CRFs can model more complex structures. The tutorial covers modeling issues in CRFs, including linear-chain CRFs, CRFs with general graphical structures, and hidden CRFs with latent variables. It also discusses inference and learning in CRFs, emphasizing the close relationship between these processes. The tutorial concludes with a discussion of related work and future directions, highlighting the importance of CRFs in structured prediction tasks.Conditional Random Fields (CRFs) are a probabilistic method for structured prediction, combining the ability of graphical models to compactly model multivariate data with the ability of classification methods to perform prediction using large sets of input features. CRFs have been widely applied in natural language processing, computer vision, and bioinformatics. This tutorial introduces CRFs, focusing on modeling, inference, and parameter estimation. It assumes no prior knowledge of graphical modeling and is intended for practitioners in various fields. CRFs model the conditional distribution $ p(\mathbf{y}|\mathbf{x}) $ directly, which is essential for classification. They are a way of combining the advantages of classification and graphical modeling, allowing for compact modeling of multivariate data and leveraging large input features. Unlike generative models, CRFs do not model the joint distribution $ p(\mathbf{y}, \mathbf{x}) $, but instead focus on the conditional distribution $ p(\mathbf{y}|\mathbf{x}) $, making them more suitable for classification tasks. CRFs can be viewed as a generalization of logistic regression and as a discriminative analog of hidden Markov models. They are particularly useful for modeling complex dependencies between output variables, such as in sequence modeling, where the output variables are arranged in a sequence. Linear-chain CRFs are a special case where the output variables form a linear chain, while general CRFs can model more complex structures. The tutorial covers modeling issues in CRFs, including linear-chain CRFs, CRFs with general graphical structures, and hidden CRFs with latent variables. It also discusses inference and learning in CRFs, emphasizing the close relationship between these processes. The tutorial concludes with a discussion of related work and future directions, highlighting the importance of CRFs in structured prediction tasks.