Traditionally, turbulence in fluid and plasma flows is studied using an Eulerian approach. This is the natural framework for studying turbulence properties like energy spectra and scaling of spatial structure functions. In recent years, triggered by advanced experimental techniques, Lagrangian statistics has gained tremendous attraction since this is the natural framework for studying transport properties. In my talk I want to analyze how spatial Eulerian fluctuations are related to temporal Lagrangian fluctuations. Special care has to be taken for analyzing Lagrangian fluctuations in compressible flows.Another open question is whether scaling properties of Eulerian longitudinal fluctuations are different from transversal ones. We start from a hierarchy of exact relations obtained by Hill (2001) and Yakhot (2001) to obtain an approximate rescaling property. This rescaling properties allow one to obtain a mapping between the probability distribution of longitudinal and transversal fluctuations.Finally, I will discuss our activities in GPU-computing and kinetic Vlasov simulations.