Rank-Up is a technique used to achieve a higher Rank Xyz Monsters through the "Rank-Up-Magic" series and "Chaos Field" in the Yu-Gi-Oh! ZEXAL anime. Fender was first one to have used this techniques through Chaos Xyz Evolution. Additionally, other than Rank-Up Xyz Monsters is "Ranking-Up a soul" which is done by denizens of Astral World, in other words, a place where 'morphing' with anyone can exist. With Astral World is a place that exists only to Rank-Up.
Double Rank-Up is a power that surpassed normal Rank-Up allowing one to Summon an Xyz monster 2 Ranks higher than the target was done by Eliphas, who's the will of Astral World. Currently, this method can only be done by "Ascension Spiral" and "Rank-Up-Magic Astral Force" so far.