A directed lattice path is a polygonal line which starts at the origin and consists of several vectors of the form (1, y) (where y belongs to a fixed set of integers) appended to each other. Enumeration of different kinds of lattice paths (walks/bridges/meanders/excursions) was accomplished by Banderier and Flajolet in 2002. We refine and generalize their results by studying lattice paths that avoid a fixed pattern (or several patterns). To this end, we develop a "vectorial kernel method" – a unified framework for enumeration of words generated by a counter automaton. Another improtant tool is the "autocorrelation polynomial" that encodes self-overlappings of a pattern, and its generalization: the "mutual correlation matrix" for several patterns. (This talk is based on joint works with Cyril Banderier, Axel Bacher, Bernhard Gittenberger and Valerie Rointer.)