Presbyopia still remains the last frontier of refractive surgery. Its surgical management is under constant evolution due to the limitations that exist today with respect to its management, which is probably in relation with the multifactorial basis in which presbyopia is clinically developed in the human. Until currently, virtually all surgical techniques that have been proposed for its correction are based on the induction of pseudoaccommodation in the presbyopic eye, including multifocality. However, the real restoration of accommodation is more complex, and it has been tried by the use of different, so called, “accommodative” pseudophakic intraocular lenses (AIOL). Overall, the reported results with these lenses by independent authors have been modest in relation with the restoration of the accommodative power of the eye and these modest benefits are usually lost with time due to the long term changes in the capsular bag. This fact made these lenses to be almost abandoned in the last few years, but there are currently other AIOL models being used with innovative mechanisms of action and different anatomical support outside the capsular bag that offer encouraging preliminary results that could bring a new potential of application to these types of lenses.In this article, we will update the modern refractive surgeon about the fundamentals and provide updated information about the outcomes of AIOLs by reviewing the concept of accommodation, the different attempts that have been accomplished in the past, their demonstrated published results in human clinical trials, and the future alternatives that may arrive in the near future.