In this talk, I will address the general problem of computing the statistical properties of stochastic dynamical systems by using probability density functions (PDF) methods. Partial differential equations for PDFs arise naturally in many different areas of mathematical physics such as particle systems (Vlasov-Poisson and Boltzmann equations), random wave theory (Malakhov-Saichev equations), stochastic dynamical systems (Liouville and Fokker-Planck equations) and turbulence theory (Lundgren-Monin-Novikov equations). These equations are also important for coarse-graining systems with a large number of degrees of freedom (Mori-Zwanzig equations). Computing the numerical solution to a PDF equation is usually a very challenging task that needs to address issues such as high-dimensionality, multiple scales, lack of regularity, conservation properties, and long-term integration. Over the years, many different techniques have been proposed to address these issues but the most efficient ones are problem-dependent. In this talk, I will review reduced-order methods for high-dimensional PDF equations, from both theoretical and numerical viewpoints. In particular, I will present two different approaches: the first one is based upon approximating the solution to PDF equations in terms of separated series expansions. This yields a hierarchy of low-dimensional equations that resembles the classical Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of kinetic gas theory. The second approach stems from techniques of irreversible statistical mechanics, i.e., the Mori-Zwanzig (MZ) projection operator method, and it relies on deriving formally exact evolution equations for the PDF of low-dimensional quantities of interest. I will address the question of approximation of MZ-PDF equations by multi-level coarse graining, perturbation series and operator cumulant resummation. Throughout the presentation I will provide numerical examples and applications of the proposed methods to prototype stochastic problems, such as the Lorenz-96 system, stochastic advection-reaction and stochastic Burgers equations.