The disclosure is directed to semiconductor structures and, more particularly, to Metal-Insulator-Metal (MIM) capacitor structures and methods of manufacture. The method includes: forming at least one gate structure; removing material from the at least one gate structure to form a trench; depositing capacitor material within the trench and at an edge or outside of the trench; and forming a first contact in contact with a first conductive material of the capacitor material and a second contact in contact with a second conductive material of the capacitor material.