Monte Carlo Sampling and Molecular Dynamics are the two most important simulation approaches for the microscopic description of phase behavior and dynamics of physical systems. As such, they are key tools for understanding what happens inside living cells, e.g., the mechanical properties of DNA molecules, and the self-assembly of membranes or protein aggregates into larger-scale structures. In this course, we discuss how to understand the physical mechanisms that govern the behavior of such biomolecules. In the first part of the course, we introduce the biological background of biopolymers and membranes and how to model these using the toolbox of statistical mechanics. The statistical mechanical context of Monte Carlo and Molecular Dynamics simulations will also be discussed. In the second part, the students apply these simulation methods to study particle-based and ensemble models for biophysical phenomena hands-on.