In many situations, both deterministic and probabilistic, one is interested in measure theory in local behaviours, for example for local dimension, entropy or Lyapunov exponents. It has been relevant to study dynamical systems, and one can develop further the study of multifractal, particularly when there exist strange attractors or repellers. Multifractal analysis in dimension refers to a notion of size, which emphasizes the local variations of the weigth of a measure. This paper gives an ammount of the literature in this field. It is also refered to the multifractal analysis of functions.