Tannins, an abundant group of plant secondary compounds, raise interest in different fields of science, owing to their unique chemical characteristics. In chemical ecology, tannins play a crucial role in plant defense against pathogens, herbivores, and changing environmental conditions. In the food industry and in medicine, tannins are important because of their proven positive effect on human health and disease treatment. Such wide interests fueled studies on tannin chemistry, especially on their flagship ability to precipitate proteins. In this Review, we expand the basic knowledge on tannin chemistry to the newest insights from the field. We focus especially on tannin reactions with different non‐protein organic N compounds, as well as the complex interactions of tannins with enzymes, resulting in either an increase or decrease in enzyme activity.