The pulsed laser deposition process is a complex one, encompassing a wide range of physical phenomena that act at different time scales, ranging from laser absorption to melting, plasma formation, and thin film deposition. In the past 15 years, there has been an exponential increase in theoretical models for different aspects of laser ablation phenomena, especially laser-produced plasmas. Among these. new types of models based on multifractal physics have been proposed. The models aim to describe the various dynamics reported for laser-produced plasmas in both the multifractal-type Schrodinger representation and in the multifractal-type hydrodynamic representation. The two approaches are complementary, as the Schrodinger representation uses operation procedures (invariance groups, variational principles, harmonic maps, etc.) while the hydrodynamic representation translates the dynamics of the laser-produced plasma into fluid motion of a multifractal type. The aim of this review is to report on the wide range of dynamics that can be discussed within the framework of a multifractal approach to plasma dynamics.