This chapter introduces character-state approaches, where sequence sites are treated as independent evolutionary characters. Maximum parsimony (MP) is explained as a method selecting the tree with the fewest evolutionary changes. Maximum likelihood (ML) is introduced as a method that uses a probabilistic framework and explicit substitution models to identify the most likely tree. Bayesian inference (BI), which uses a likelihood framework but differs from ML in that it incorporates prior probabilities in calculating posterior probabilities, is also discussed. The Markov chain Monte Carlo approach is explained with respect to estimating the posterior probability of a tree. Detailed worked examples comparing MP and ML are illustrated to highlight the difference between parsimony and likelihood-based methods.