K (KCNK) potassium channels form "background" or "leak" currents that have critical roles in cell excitability control in the brain, cardiovascular system, and somatosensory neurons. Similar to many ion channel families, studies of Ks have been limited by poor pharmacology. Of six K subfamilies, the thermo- and mechanosensitive TREK subfamily comprising K2.1 (TREK-1), K4.1 (TRAAK), and K10.1 (TREK-2) are the first to have structures determined for each subfamily member. These structural studies have revealed key architectural features that underlie K function and have uncovered sites residing at every level of the channel structure with respect to the membrane where small molecules or lipids can control channel function. This polysite pharmacology within a relatively small (~70 kDa) ion channel comprises four structurally defined modulator binding sites that occur above (Keystone inhibitor site), at the level of (K modulator pocket), and below (Fenestration and Modulatory lipid sites) the C-type selectivity filter gate that is at the heart of K function. Uncovering this rich structural landscape provides the framework for understanding and developing subtype-selective modulators to probe K function that may provide leads for drugs for anesthesia, pain, arrhythmia, ischemia, and migraine.