Depression and anxiety are severe public health problems and have attracted more and more attention from researchers of food science and nutrition. Dietary natural products and nutrients, such as fish, coffee, tea, n-3 PUFA, lycopene, and dietary fiber, could play a vital role in the prevention and management of these diseases. The potential mechanisms of action mainly include inhibiting inflammation, ameliorating oxidative stress, modulating the microbiota-gut-brain axis, suppressing hypothalamic-pituitary-adrenal axis hyperactivity, and regulating the levels of monoamine neurotransmitters. In this narrative review, we summarize the most recent advancements regarding the effects of dietary natural products and nutrients on depression and anxiety, and their underlying mechanisms are discussed. We hope that this paper can provide a better understanding of the anti-depressive and anxiolytic action of dietary natural products, and that it is also helpful for developing dietary natural products for functional food, dietary supplements, or auxiliary agents for the prevention and management of these diseases.