Biological systems generally rely on various active (non-equilibrium) processes to perform their vital functions. Examples include homeostasis, cell migration and adhesion, and the formation of cellular aggregates. The main goal of our research is to understand and describe the physical mechanisms which govern different biological processes, and link them to relevant biological functions. For this purpose, we employ numerical simulations and analytical modelling. In this talk, I will give a few examples from our research concerning non-equilibrium processes in biological systems. First, I will show non-equilibrium membrane fluctuations of a red blood cell, which may result from the interactions between a lipid membrane and the cell's cytoskeleton as well as from the activity of intramembrane pumps. The second example will illustrate transient detachment of a cell membrane from its bulk cytoskeleton due to a cytoskeletal contraction, which leads to the formation of blebs. Finally, I will discuss aggregation of platelets and the highly adhesive protein von Willebrand factor (VWF) in the hemostatic process (i.e., blood clotting) and, in particular, the regulation of VWF.