Proton therapy (PT) has the potential to deliver conformal doses to the tumor while sparing normal tissue, but is highly susceptible to treatment uncertainties. The occurrence of anatomical changes during PT treatments has a major impact on the delivered dose, often necessitating plan adaptations that are typically performed offline and require a few days before the adapted plan is ready. In order to react promptly to detected anatomical changes, online adaptive proton therapy (OAPT) has been proposed with the goal of adapting the plan while the patient is on the treatment couch. First OAPT workflows for daily plan adaptation that are effective against interfractional anatomical variations have reached clinical application. However, even faster OAPT workflows are needed to cope with faster anatomical changes. Near real-time adaptive PT (NAPT) relying on online in vivo treatment verification can be a potential solution for many tumor entities (e.g., thoraco-abdominal tumors), which would greatly benefit from the conformality of PT, but are presently challenging to treat with proton beams due to the influence of intrafractional variations. In addition, NAPT offers the opportunity to achieve the long-awaited closed PT feedback loop. In this paper we review the required tasks and necessary components in an OAPT workflow for the application of near real-time adaptation, proceeding sequentially from volumetric imaging for online plan adaptation up to online verification during delivery. Available technology and upcoming developments are discussed. Several aspects regarding regulatory approval, cost-benefit related issues and additional beyond-the-loop tasks are also addressed.