Mammals contain 28 genes encoding Transient Receptor Potential (TRP) proteins. The proteins assemble into cationic channels, often with calcium permeability. Important roles in physiology and disease have emerged and so there is interest in whether the channels might be suitable therapeutic drug targets. Here we review selected members of three subfamilies of mammalian TRP channel (TRPC5, TRPM2 and TRPA1) that show relevance to sensing of adversity by cells and biological systems. Summarized are the cellular and tissue distributions, general properties, endogenous modulators, protein partners, cellular and tissue functions, therapeutic potential, and pharmacology. TRPC5 is stimulated by receptor agonists and other factors that include lipids and metal ions; it heteromultimerises with other TRPC proteins and is involved in cell movement and anxiety control. TRPM2 is activated by hydrogen peroxide; it is implicated in stress-related inflammatory, vascular and neurodegenerative conditions. TRPA1 is stimulated by a wide range of irritants including mustard oil and nicotine but also, controversially, noxious cold and mechanical pressure; it is implicated in pain and inflammatory responses, including in the airways. The channels have in common that they show polymodal stimulation, have activities that are enhanced by redox factors, are permeable to calcium, and are facilitated by elevations of intracellular calcium. Developing inhibitors of the channels could lead to new agents for a variety of conditions: for example, suppressing unwanted tissue remodeling, inflammation, pain and anxiety, and addressing problems relating to asthma and stroke.