The rapid advances of science and technology have provided a large part of the world with all conceivable needs and comfort. However, this welfare comes with serious threats to the planet and many of its inhabitants. An enormous amount of scientific evidence points at global warming, mass destruction of bio-diversity, scarce resources, health risks, and pollution all over the world. These facts are generally acknowledged nowadays, not only by scientists, but also by the majority of politicians and citizens. Nevertheless, this understanding has caused insufficient changes in our decision making and behavior to preserve our natural resources and to prevent upcoming (natural) disasters. In the present study, we try to explain how systematic tendencies or distortions in human judgment and decision-making, known as "cognitive biases," contribute to this situation. A large body of literature shows how cognitive biases affect the outcome of our deliberations. In natural and primordial situations, they may lead to quick, practical, and satisfying decisions, but these decisions may be poor and risky in a broad range of modern, complex, and long-term challenges, like climate change or pandemic prevention. We first briefly present the social-psychological characteristics that are inherent to (or typical for) most sustainability issues. These are: experiential vagueness, long-term effects, complexity and uncertainty, threat of the status quo, threat of social status, personal vs. community interest, and group pressure. For each of these characteristics, we describe how this relates to cognitive biases, from a neuro-evolutionary point of view, and how these evolved biases may affect sustainable choices or behaviors of people. Finally, based on this knowledge, we describe influence techniques (interventions, nudges, incentives) to mitigate or capitalize on these biases in order to foster more sustainable choices and behaviors.