Cataract surgery has become a refractive procedure in which emmetropia is the goal, with the implantation of extended depth-of-focus or multifocal intraocular lenses (IOLs) being the commonly selected option to restore vision beyond the far distance. The selection criteria for implanting these lenses can differ from those for monofocal IOLs and even between technologies, as eye characteristics can affect postoperative visual performance. Corneal astigmatism is an eye characteristic that can affect visual performance differently, depending on the implanted IOL. The magnitude of corneal astigmatism, the tolerance of the IOL to this astigmatism, economic aspects, comorbidities, and the efficacy of astigmatism treatment are factors that can make surgeons’ doubt as to what astigmatism treatment should be applied to each patient. This review aims to summarize the current evidence related to low astigmatism tolerance in presbyopia-correcting lenses, the efficacy achieved through corneal incisions, and their comparison with the implantation of toric IOLs.Supplementary InformationThe online version contains supplementary material available at 10.1186/s12886-023-03003-2.