Towards multifractional calculus

6 pags. -- Open Access funded by Creative Commons Atribution Licence 4.0After motivating the need of a multiscale version of fractional calculus in quantum gravity, we review current proposals and the program to be carried out in order to reach a viable definition of scale-dependent fractional operators. We present different types of multifractional Laplacians and comment on their known or expected properties.The author is under a Ramón y Cajal contract and is supported by the I+D grants FIS2014-54800-C2-2-P and FIS2017-86497- C2-2-P.Peer Reviewe