The brain is constantly adapting to a changing environment. It detects environmental stimuli, integrates that information with internal states, and engages appropriate behavioral and physiological responses. This process of stability through change is termed “allostasis”, and serves as a mechanism by which an organism can adapt to a changing environment to function optimally, and ultimately ensure survival. The ability to adapt to stressors in the environment by “bending” but not “breaking” can be considered as “resilience”. Individuals that are more able to withstand such challenges to their stability, and bounce back after, can be considered more resilient than those that do not. This review will explore what resilience means in a neurobiological context, the role of stress and allostasis, and focuses on the role of neurotrophins, particularly BDNF, in mediating adaptive plasticity.