The majority of mammalian genomes are devoted to transposable elements (TEs). Whilst TEs are increasingly recognized for their important biological functions, they are a potential danger to genomic stability and are carefully regulated by the epigenetic system. However, the full complexity of this regulatory system is not understood. Here, using mouse embryonic stem cells, we show that TEs are suppressed by heterochromatic marks like H3K9me3, and are also labelled by all major types of chromatin modification in complex patterns, including bivalent activatory and repressive marks. We identified 29 epigenetic modifiers that significantly deregulated at least one type of TE. The loss of Setdb1, Ncor2, Rnf2, Kat5, Prmt5, Uhrf1, and Rrp8 caused widespread changes in TE expression and chromatin accessibility. These effects were context-specific, with different chromatin modifiers regulating the expression and chromatin accessibility of specific subsets of TEs. Our work reveals the complex patterns of epigenetic regulation of TEs.