This contribution reviews the nonlinear stochastic properties of turbulent velocity and passive scalar intermittent fluctuations in Eulerian and Lagrangian turbulence. These properties are illustrated with original data sets of (i) velocity fluctuations collected in the field and in the laboratory, and (ii) temperature, salinity and in vivo fluorescence (a proxy of phytoplankton biomass, i.e. unicelled vegetals passively advected by turbulence) sampled from highly turbulent coastal waters. The strength of three of the most popular models describing intermittent fluctuations (the lognormal, log-Lévy and log-Poisson models) to fit the distribution of in vivo fluorescence has subsequently been critically assessed. A theoretical formulation for the stochastic properties of biologically active scalars is also provided and validated. Finally, the potential effect of the intermittent properties of turbulent velocity fluctuations on processes relevant to the life of plankton organisms are theoretically investigated. It is shown that the intermittent nature of microscale turbulence may result in (i) a decrease in the rate of nutrient fluxes towards non-motile phytoplankton cells (6-62 %), (ii) a decrease in the physical coagulation of phytoplankton cells (25-48 %) and in the subsequent phytoplankton aggregate volumes (22-41 %), and (iii) a decrease of the turbulence contribution to predator-prey encounter rates (25-50 %).