Protein kinases are one of the most studied drug targets in current pharmacological research, as evidenced by the vast number of kinase-targeting agents enrolled in active clinical trials. Dual-specificity Tyrosine phosphorylation-Regulated Kinase 1A (DYRK1A) has been much less studied compared to many other kinases. DYRK1A primary function occurs during early development, where this protein regulates cellular processes related to proliferation and differentiation of neuronal progenitor cells. Although most extensively characterised for its role in brain development, DYRK1A is over-expressed in a variety of diseases including a number of human malignancies, such as haematological and brain cancers. Here we review the accumulating molecular studies that support our understanding of how DYRK1A signalling could underlie these pathological functions. The relevance of DYRK1A in a number of diseases is also substantiated with intensive drug discovery efforts to develop potent and selective inhibitors of DYRK1A. Several classes of DYRK1A inhibitors have recently been disclosed and some molecules are promising leads to develop DYRK1A inhibitors as drugs for DYRK1A-dependent diseases.