Biological sequence analysis is based on discrete statistical models coupled with efficient algorithms for parameter estimation and statistical inference. Over the past 10 years methods from abtract algebra and algebraic geometry have been applied increasingly to the analysis of statistical models giving rise to the new field of algebraic statistics. We will introduce some basic ideas of algebraic statistics and illustrate its application to statistical models of sequnce evolution. In particular, we discuss the connection between parametric sequence alignment and tropical geometry, and the algebraic invariants of mutagenetic trees.