Statistical learning problems arise in the study of molecular evolution as well as in the development of gene predictors. Problems can be unsupervised, supervised or partially supervised in nature depending on the situation. This talk will discuss the use of oligonucleotide distributions in DNA sequences in solving such problems. Some related probabilistic models for DNA sequences will also be discussed. In particular, a stochastic replication model for biological sequences will be introduced that generalizes standard hidden Markov models.