Damping is a critical design parameter for miniaturized mechanical resonators usedin microelectromechanical systems (MEMS), nanoelectromechanical systems (NEMS),optomechanical systems, and atomic force microscopy for a large and diverse set ofapplications ranging from sensing, timing, and signal processing to precisionmeasurements for fundamental studies of materials science and quantum mechanics.This paper presents an overview of recent advances in damping from the viewpointof device design. The primary goal is to collect and organize methods, tools, andtechniques for the rational and effective control of linear damping in miniaturizedmechanical resonators. After reviewing some fundamental links between dynamicsand dissipation for systems with small linear damping, we explore the space ofdesign and operating parameters for micromechanical and nanomechanicalresonators; classify the mechanisms of dissipation into fluid–structure interactions(viscous damping, squeezed-film damping, and acoustic radiation), boundarydamping (stress-wave radiation, microsliding, and viscoelasticity), and materialdamping (thermoelastic damping, dissipation mediated by phonons and electrons,and internal friction due to crystallographic defects); discuss strategies for minimizingeach source using a combination of models for dissipation and measurements of material properties; and formulate design principles for low-loss micromechanical and nanomechanical resonators