The dinucleotide (a cytosine followed by a guanine on a single DNA strand) has a pattern of non-homogeneity along the genome. Regions of relatively low frequencies are interrupted by clusters with markedly higher and content, known as islands (CGI). CGI are often associated with the promoter regions of genes, and methylation of the promoter CGI is associated with the transcriptional silence of the gene. Conversely, promoter-associated CGI in constitutively-expressed housekeeping genes are unmethylated. Appropriate methylation of CGIs is required for normal development, and inappropriate methylation of CGI in tumor suppressor promoters has been associated with the development of numerous human cancers. We introduce hidden Markov chains as a modeling tool in DNA sequence analysis and discuss the use of such models for island identification. We describe the canonical problems of decoding, evaluation, and training for Hidden Markov Models, and discuss the following algorithms that provide solutions to those problems: Viterbi decoding, the forward-backward algorithm, posterior decoding, and the Baum-Welch algorithm. The chapter contains numerous examples and exercises many of which utilize the specialized companion suite of web applications CpG Educate developed for this chapter and available at http://cpgeducate.com/.