Allelic imbalance (AI) is a phenomenon where the two alleles of a given gene are expressed at different levels in a given cell, either because of epigenetic inactivation of one of the two alleles, or because of genetic variation in regulatory regions. Recently, Bing et al. have described the use of genotyping arrays to assay AI at a high resolution (approximately 750,000 SNPs across the autosomes). In this paper, we investigate computational approaches to analyze this data and identify genomic regions with AI in an unbiased and robust statistical manner. We propose two families of approaches: (i) a statistical approach based on z-score computations, and (ii) a family of machine learning approaches based on Hidden Markov Models. Each method is evaluated using previously published experimental data sets as well as with permutation testing. When applied to whole genome data from 53 HapMap samples, our approaches reveal that allelic imbalance is widespread (most expressed genes show evidence of AI in at least one of our 53 samples) and that most AI regions in a given individual are also found in at least a few other individuals. While many AI regions identified in the genome correspond to known protein-coding transcripts, others overlap with recently discovered long non-coding RNAs. We also observe that genomic regions with AI not only include complete transcripts with consistent differential expression levels, but also more complex patterns of allelic expression such as alternative promoters and alternative 3 end. The approaches developed not only shed light on the incidence and mechanisms of allelic expression, but will also help towards mapping the genetic causes of allelic expression and identify cases where this variation may be linked to diseases.