DNA molecules have several structural features that allow DNA to be used as tools for solving computational problems. Some of these same features of DNA molecules allow them to generate, in the presence of appropriate enzymes, potentially infinite ‘languages’ over the alphabet of paired nucleotides A/T, C/G, G/C and T/A. Fundamental features of DNA are described in detail. Language generation, via ‘splicing systems’, is then described at some length. Then, in three short Sections, computations of solutions of toy instances of classical combinatorial problems are indicated with references given for detailed study. We close with an invitation to investigate the exciting new work in DNA constructions and computations through the web pages of several researchers. These notes were prepared to accompany tutorial talks given at the 1st Intern. Work Confer. on Linguistics, Biology and Computer Science: Interplays in Tarragona, Spain March 14–19, 2011.