Recurrent DNA copy number alterations (CNA) are widely studied in diagnostic and cytogenetic cancer research. CNAs reveal locations that may alter gene dosage and thus expression of the genes contained within. Array comparative genomic hybridization has emerged as a popular high-throughput, genome-wide technique to interrogate tumor genomes for copy number alterations. When studying a group of tumors derived from a patient cohort, it is of great interest to detect the copy number alterations that are common across the population and thus assumed to be potential diagnostic markers and/or predictors of clinical outcome. In this paper, we review extant and available computational approaches for detecting such recurrent copy number alterations from array comparative genomic hybridization (aCGH) data. This is a challenging computational problem due to various sources of noise in the data that can obscure the recurrent copy number signals or induce false positives in their prediction. In this paper, we qualitatively evaluate methods designed to detect recurrent copy number alterations for aCGH data based on their analytical strengths and limitations, and discuss expected future directions in this important area of cancer research. Copyright 2009 S. Karger AG, Basel.