N6-methyladenosine (m6A) is the most prevalent internal RNA modification in eukaryotic messenger RNAs (mRNAs), regulating gene expression at the transcription and post-transcription levels. Complex interplay between m6A and other well-studied epigenetic modifications, including histone modifications and DNA modification, has been extensively reported in recent years. The crosstalk between RNA m6A modification and histone/DNA modifications plays a critical role in establishing the chromatin state for the precise and specific fine-tuning of gene expression and undoubtedly has profound impacts on both physiological and pathological processes. In this review, we discuss the crosstalk between RNA m6A modification and histone/DNA modifications, emphasizing their sophisticated communications and the mechanisms underlying to gain a comprehensive view of the biological relevance of m6A-based epigenetic network.