Understanding the intriguing complexity of living systems is one of the main driving forces of science. To gain insight we use biomimetic systems that reconstitute well defined cellular assemblies and compare these to the living system. Our main interests are the mechanical properties and the generation of forces, both mediated by the cytoskeleton and its interaction with the plasma membrane. Recent advances allow to mimic structures such as the actin cortex, sparse actin networks and actin bundles, and we use optical tweezers to quantify the mechanical properties of these structures and to compare them to living cells. While sparse actin networks and polymerizing actin bundles show rather passive behavior, we find clear signs of activity that drives the red blood cell membrane fluctuation. Our studies of the mechanical fluctuation and the mechanical response function reveals a violation of the dissipation fluctuation theorem, which in turn shows that the red blood cell membrane fluctuations should be described as a process that is out of the thermodynamic equilibrium.