The interest in medicinal and aromatic plants (MAPs) has increased significantly in recent years, driven by the growing demand for natural products. MAPs are a valuable source of secondary metabolites, which renders them useful to a number of industries, including cosmetics, pharmaceuticals, and food. The Lamiaceae family includes economically important MAPs that produce valuable secondary metabolites such as essential oils (EOs) and phenolic compounds (PCs). The quantity and quality of these secondary metabolites are affected by abiotic stress factors. In a climate change scenario, the Lamiaceae is one of the most affected families, especially due to its wide distribution in the Mediterranean region. In the present study, the most common climate-related environmental stress factors, namely, drought, salinity, temperature, light, and heavy metals, were reviewed and discussed in order to assess their impact on the chemical profiles of EOs and PCs, as well as on the biological properties (antioxidant, antibacterial, antimelanogenic, pest-repellent, and UV-protective) of Lamiaceae species. It can be posited that these stresses typically act as a catalyst for the secondary metabolism of these plants, resulting in increased production of EO compounds (e.g., 1,8-cineole, linalool, camphor, borneol, and limonene) and PCs (e.g., rosmarinic, caffeic, and salvianolic acids) and subsequent enhancement of their biological activities. In view of the industrial applications of these bioactive compounds, it is of interest to explore the changes in secondary metabolism induced by environmental factors as it is possible to increase the accumulation of valuable secondary metabolites.