Background: During early embryonic development, one of the two X chromosomes in mammalian female cells is inactivated to compensate for a potential imbalance in transcript levels with male cells, which contain a single X chromosome. Here, we use mouse female embryonic stem cells (ESCs) with non-random X chromosome inactivation (XCI) and polymorphic X chromosomes to study the dynamics of gene silencing over the inactive X chromosome by high-resolution allele-specific RNA-seq. Results: Induction of XCI by differentiation of female ESCs shows that genes proximal to the X-inactivation center are silenced earlier than distal genes, while lowly expressed genes show faster XCI dynamics than highly expressed genes. The active X chromosome shows a minor but significant increase in gene activity during differentiation, resulting in complete dosage compensation in differentiated cell types. Genes escaping XCI show little or no silencing during early propagation of XCI. Allele-specific RNA-seq of neural progenitor cells generated from the female ESCs identifies three regions distal to the X-inactivation center that escape XCI. These regions, which stably escape during propagation and maintenance of XCI, coincide with topologically associating domains (TADs) as present in the female ESCs. Also, the previously characterized gene clusters escaping XCI in human fibroblasts correlate with TADs. Conclusions: The gene silencing observed during XCI provides further insight in the establishment of the repressive complex formed by the inactive X chromosome. The association of escape regions with TADs, in mouse and human, suggests that TADs are the primary targets during propagation of XCI over the X chromosome.