Free‐electron lasers (FELs) are currently under intense research and development throughout the world for a variety of applications. A number of physics issues place limits on the performance of FELs. These include, among others, i) the generation of high quality, high current electron beams, ii) optical guiding of the generated radiation beam, iii) undulator field errors, and iv) the excitation of sideband radiation. The goal of this paper is to review and discuss these FEL physics issues. The most important component of an FEL is a high quality electron beam. For efficient operation the effective electron beam energy spread must be sufficiently small. The effective energy spread is determined by i) transverse beam emittance, ii) undulator transverse spatial gradients, iii) undulator field error effects, iv) beam space‐charge effects, v) intrinsic energy spread, and vi) energy stability. Another important aspect of FEL operation is optical guiding of the generated radiation beam. In many proposed FEL experiments, the short wavelength radiation beam will note be confined by a waveguide structure, and the interaction length is required to be long compared to the free‐space Rayleigh (diffraction) length. Optical guiding of the generated radiation can, therefore, play a central role in the practical utilization of FELs. However, optical guiding imposes limits on several FEL parameters. These, as well as other constraints, will be discussed in detail, and theoretical criteria and numerical simulations will be presented.