Electrons are quantum-mechanical particles that are strongly repelled from each other by the Coulomb interaction. While introductory physics courses focus on the Coulombic force and neglect the quantum mechanics, a typical metal (such as copper) can be modeled quite well by treating the quantum mechanics and ignoring interactions. However, quantum mechanics and interactions are both essential for understanding quantum dots: nanometer-to-micron-scale boxes engineered to trap electrons. The spatial confinement means that a dot has discrete energy levels very much like those of an atom, with the advantage that the shape, size, and connection of the quantum dot to the outside world can all be tuned. Perhaps surprisingly given its greater size, a quantum dot generally exhibits stronger manifestations of electron-electron repulsion than are found in atoms, including the experimental ability to change the number of dot electrons one by one, and the creation of induced long-range interactions between otherwise-free electrons in metallic leads connected to the dot (the Kondo effect). Devices containing two or more dots can exhibit quantum interference between different electron paths through a device. Interference and other quantum phenomena can produce phase transitions at the absolute zero of temperature that produce physical properties at finite temperatures unlike any seen in normal metals. Multi-dot devices lie at the heart of proposals for future electronic devices and quantum computers.