The concept of using single molecules as key building blocks for logic gates, diodes and transistors to perform basic functions of digital electronic devices at the molecular scale has been explored over the past decades. However, in addition to mimicking the basic functions of current silicon devices, molecules often possess unique properties that have no parallel in conventional materials and promise new hybrid devices with novel functions that cannot be achieved with equivalent solid-state devices. The most appealing example is the molecular switch. Over the past decade, molecular switches on surfaces have been intensely investigated. A variety of external stimuli such as light, electric field, temperature, tunneling electrons and even chemical stimulus have been used to activate these molecular switches between bistable or even multiple states by manipulating molecular conformations, dipole orientations, spin states, charge states and even chemical bond formation. The switching event can occur either on surfaces or in break junctions. The aim of this review is to highlight recent advances in molecular switches triggered by various external stimuli, as investigated by low-temperature scanning tunneling microscopy (LT-STM) and the break junction technique. We begin by presenting the molecular switches triggered by various external stimuli that do not provide single molecule selectivity, referred to as non-selective switching. Special focus is then given to selective single molecule switching realized using the LT-STM tip on surfaces. Single molecule switches operated by different mechanisms are reviewed and discussed. Finally, molecular switches embedded in self-assembled monolayers (SAMs) and single molecule junctions are addressed.