Research has resulted in regulatory approval of nine agents for acute myeloid leukaemia indications by the US Food and Drug Administration since 2017: the Bcl-2 inhibitor, venetoclax; two FLT3 inhibitors, midostaurin and gilteritinib; two IDH inhibitors, ivosidenib (IDH1 inhibitor) and enasidenib (IDH2 inhibitor); the anti-CD33 antibody-drug conjugate, gemtuzumab ozogamicin; the oral, poorly absorbable hypomethylating agent, azacitidine; the liposomal formulation of cytarabine and daunorubicin (5:1 ratio), CPX-351; and the hedgehog signalling pathway inhibitor, glasdegib. A 100% absorbable oral formulation of the hypomethylating agent decitabine was approved for the treatment of myelodysplastic syndrome and chronic myelomonocytic leukaemia, and might be used as an alternative to parenteral hypomethylating agents. Several of the approvals are as single-agent therapies or in specific combinations for narrow indications, thus offering poor treatment value. In this Review, we discuss ongoing research into combinations containing these commercially available targeted therapies for acute myeloid leukaemia., Competing Interests: Declaration of interests HK reports research grants and honoraria from AbbVie, Amgen, Ascentage, Bristol Myers Squibb, Daiichi-Sankyo, Immunogen, Jazz Pharmaceuticals, Novartis, Pfizer, and Sanofi, and honoraria from Actinium (Advisory Board), Adaptive Biotechnologies, Aptitude Health, BioAscend, Delta Fly, Janssen Global, Oxford Biomedical, and Takeda Oncology. AW has served on advisory boards for Novartis, Janssen, Amgen, Roche, Pfizer, AbbVie, Servier, Celgene (Bristol Myers Squibb), Macrogenics, Agios, and Gilead Sciences, receives research funding from Novartis, AbbVie, Servier, Celgene (Bristol Myers Squibb), AstraZeneca, and Amgen, serves on speakers bureaus for AbbVie, Novartis, and Celgene, and receives royalty payments from the Walter and Eliza Hall Institute of Medical Research related to venetoclax. MT has served on advisory boards for AbbVie, Daiichi-Sankyo, Orsenix, Kahr, Delta Fly Pharma, Jazz Pharmaceuticals, Roche, Biosight, Novartis, Innate Pharmaceuticals, Kura Oncology, and Syros Pharmaceuticals, received research funding from AbbVie, Orsenix, Biosight, Glycomimetics, Rafael Pharmaceuticals, and Amgen, and received royalty from UpToDate. NJS has received consulting fees from Takeda Oncology and AstraZeneca, research funding from Takeda Oncology and Astellas Pharma, and honoraria from Amgen. ESW has served on advisory boards for AbbVie, Astellas, Celgene (Bristol Myers Squibb), Genentech, GlaxoSmithKline, Jazz Pharmaceuticals, Kite Pharmaceuticals, Kura Oncology, Novartis, Pfizer, Stemline, and Takeda, provided consulting for Mana Therapeutics, served as a speaker for Stemline, Kura Oncology, Pfizer, and Dava Oncology, and served on data safety monitoring committees for AbbVie and Rafael Pharmaceuticals. CDiN received research funding from AbbVie, Agios, Calithera, Cleave, Celgene (Bristol Myers Squibb), Daiichi-Sankyo, Forma, ImmuneOnc, and Loxo, consultancy fees from AbbVie, Agios, Aprea, Celgene/Bristol Myers Squibb, ImmuneOnc, and advisory board fees from Novartis, Aprea and Takeda. She is a scientific advisor with stock options from Notable Labs. AEP received research funding from AbbVie, Actinium Pharmaceuticals, Astellas, Daiichi-Sankyo, and FujiFilm, and received consultancy or advisory fees from AbbVie, Actinium Pharmaceuticals, Astellas, Celgene (Bristol Myers Squibb), Genentech, Daiichi-Sankyo, Loxo, Syndax, Sumitomo Dainippon, Forma, and Onconova. EMS received research funding from Agios, Celgene, Bristol Myers Squibb, Syndax, Syros, Bayer, and Biotheryx, and has served in a consulting or advisory role fees for Daiichi-Sankyo, Bristol Myers Squibb, Celgene, Agios, Novartis, AbbVie, Astellas, Genentech, Syndax, Gilead Sciences, Amgen, Foghorn, Neoleukin, Pinotbio, and Blueprint. ND has received research funding from Daiichi-Sankyo, Bristol Myers Squibb, Pfizer, Gilead Sciences, Sevier, Genentech, Astellas, AbbVie, Hanmi, Trovagene, Fate Therapeutics, Amgen, Novimmune, Glycomimetics, Trillium, and ImmunoGen, and has served in a consulting or advisory role for Daiichi-Sankyo, Bristol Myers Squibb, Arog, Pfizer, Novartis, Jazz Pharmaceuticals, Celgene, AbbVie, Astellas, Genentech, Immunogen, Servier, Syndax, Trillium, Gilead Sciences, Amgen, Shattuck Labs, and Agios. We declare no other competing interests., (Copyright © 2021 Elsevier Ltd. All rights reserved.)