Acute myeloid leukemia (AML) is a malignant tumor of the immature myeloid hematopoietic cells in the bone marrow (BM). It is a highly heterogeneous disease, with rising morbidity and mortality in older patients. Although researches over the past decades have improved our understanding of AML, its pathogenesis has not yet been fully elucidated. Long noncoding RNAs (lncRNAs), microRNAs (miRNAs), and circular RNAs (circRNAs) are three noncoding RNA (ncRNA) molecules that regulate DNA transcription and translation. With the development of RNA-Seq technology, more and more ncRNAs that are closely related to AML leukemogenesis have been discovered. Numerous studies have found that these ncRNAs play an important role in leukemia cell proliferation, differentiation, and apoptosis. Some may potentially be used as prognostic biomarkers. In this systematic review, we briefly described the characteristics and molecular functions of three groups of ncRNAs, including lncRNAs, miRNAs, and circRNAs, and discussed their relationships with AML in detail.