This chapter introduces Conditional Random Fields (CRFs) for relational learning. CRFs are conditional probability models that directly model the distribution of output variables given input variables, making them suitable for classification tasks. Unlike traditional graphical models that model the joint distribution of variables, CRFs focus on the conditional distribution, allowing for the use of rich, global features without explicitly modeling dependencies among input variables. This makes CRFs particularly effective for tasks involving relational data, such as natural language processing, bioinformatics, and computer vision. The chapter begins with an overview of graphical models, discussing their role in representing probability distributions over sets of random variables. It then compares generative models, such as naive Bayes and logistic regression, with discriminative models like CRFs, highlighting the advantages of discriminative modeling in capturing complex dependencies among output variables. The chapter then introduces linear-chain CRFs, which are a special case of CRFs designed for sequence modeling. These models are motivated by hidden Markov models (HMMs) and are used for tasks such as named-entity recognition. The chapter explains how linear-chain CRFs can be extended to general CRFs with more complex graphical structures, allowing for the modeling of long-distance dependencies between labels. The chapter also discusses parameter estimation and inference techniques for CRFs, including maximum likelihood estimation with regularization and efficient inference algorithms such as forward-backward and Viterbi. These methods enable the training of CRFs on large datasets and the accurate prediction of labels for new instances. Finally, the chapter presents various applications of CRFs across different domains, including text processing, bioinformatics, and computer vision. It highlights the versatility of CRFs in handling relational data and their effectiveness in tasks such as information extraction, named-entity recognition, and object recognition. The chapter concludes by emphasizing the importance of CRFs in modern machine learning for their ability to model complex dependencies and provide accurate predictions in a wide range of applications.This chapter introduces Conditional Random Fields (CRFs) for relational learning. CRFs are conditional probability models that directly model the distribution of output variables given input variables, making them suitable for classification tasks. Unlike traditional graphical models that model the joint distribution of variables, CRFs focus on the conditional distribution, allowing for the use of rich, global features without explicitly modeling dependencies among input variables. This makes CRFs particularly effective for tasks involving relational data, such as natural language processing, bioinformatics, and computer vision. The chapter begins with an overview of graphical models, discussing their role in representing probability distributions over sets of random variables. It then compares generative models, such as naive Bayes and logistic regression, with discriminative models like CRFs, highlighting the advantages of discriminative modeling in capturing complex dependencies among output variables. The chapter then introduces linear-chain CRFs, which are a special case of CRFs designed for sequence modeling. These models are motivated by hidden Markov models (HMMs) and are used for tasks such as named-entity recognition. The chapter explains how linear-chain CRFs can be extended to general CRFs with more complex graphical structures, allowing for the modeling of long-distance dependencies between labels. The chapter also discusses parameter estimation and inference techniques for CRFs, including maximum likelihood estimation with regularization and efficient inference algorithms such as forward-backward and Viterbi. These methods enable the training of CRFs on large datasets and the accurate prediction of labels for new instances. Finally, the chapter presents various applications of CRFs across different domains, including text processing, bioinformatics, and computer vision. It highlights the versatility of CRFs in handling relational data and their effectiveness in tasks such as information extraction, named-entity recognition, and object recognition. The chapter concludes by emphasizing the importance of CRFs in modern machine learning for their ability to model complex dependencies and provide accurate predictions in a wide range of applications.