Engines and motors are everywhere in the modern world, but it is a challenge to make them work if they are very small. On the micron length scale, inertial forces are weak and conventional motor designs involving, e.g., pistons, jets, or flywheels cease to function. Biological motors work by a different principle, using catalysis to convert chemical to mechanical energy on the nanometer length scale. To do this, they must apply force continuously against their viscous surroundings, and because of their small size, their movement is "jittery" because of the random shoves and turns they experience from molecules in their surroundings. The first synthetic catalytic motors, discovered about 15 years ago, were bimetallic Pt-Au microrods that swim in fluids through self-electrophoresis, a mechanism that is apparently not used by biological catalytic nanomotors. Despite the difference in propulsion mechanisms, catalytic microswimmers are subject to the same external forces as natural swimmers such as bacteria. Therefore, they follow similar scaling laws, are subject to Brownian forces, and exhibit a rich array of biomimetic emergent behavior (e.g., chemotaxis, rheotaxis, schooling, and predator-prey behavior). It was later discovered, quite by accident, that the same metallic microrods undergo rapid autonomous movement in acoustic fields, converting excitation energy in the frequency (MHz) and power range (up to several W/cm2) that is commonly used for ultrasonic imaging into axial movement. Because the acoustic propulsion mechanism is fuel-free, it can operate in media that have been inaccessible to chemically powered motors, such as the interior of living cells. The power levels used are intermediate between those of ultrasonic diagnostic imaging and therapy, so the translation of basic research on microswimmers into biomedical applications, including in vivo diagnostics and drug delivery, is possible. Acoustic and chemical propulsion are applied independently to microswimmers, so by modulating the acoustic power one can achieve microswimmer functionalities that are not accessible with the individual propulsion mechanisms. These include motion of particles forward and backward with switching between chemical and acoustic propulsion, the assembly/disassembly equilibrium of particle swarms and colloidal molecules, and controllable upstream or downstream propulsion in a flowing fluid. This Account relates our current understanding of the chemical and acoustic propulsion mechanisms, and describes how their combination can be particularly powerful for imparting enhanced functionality to micromotors.