Down syndrome (DS), the most common genetic cause of intellectual disability, is caused by the trisomy of chromosome 21. MNB/DYRK1A (Minibrain/dual specificity tyrosine phosphorylation-regulated kinase 1A) has possibly been the most extensively studied chromosome 21 gene during the last decade due to the remarkable correlation of its functions in the brain with important DS neuropathologies, such as neuronal deficits, dendrite atrophy, spine dysgenesis, precocious Alzheimer's-like neurodegeneration, and cognitive deficits. MNB/DYRK1A has become an attractive drug target because increasing evidence suggests that its overexpression may induce DS-like neurobiological alterations, and several small-molecule inhibitors of its protein kinase activity are available. Here, we summarize the functional complexity of MNB/DYRK1A from a DS-research perspective, paying particular attention to the capacity of different MNB/DYRK1A inhibitors to reverse the neurobiological alterations caused by the increased activity of MNB/DYRK1A in experimental models. Finally, we discuss the advantages and drawbacks of possible MNB/DYRK1A-based therapeutic strategies that result from the functional, molecular, and pharmacological complexity of MNB/DYRK1A.