Most waveguides for millimeter wavelengths are partly or fully open, sometimes in view of their low-loss design but usually because they are employed in integrated-circuit fashion. The open nature of these waveguides can cause leakage that results in cross-talk between neighboring components, in the lowering of circuit Q, or in the outright loss of power. Such leakage can be produced by several different basic mechanisms, including radiation from waveguide discontinuities into surface waves, space waves, or leaky below-cutoff higher modes of the open waveguides themselves, or by continuous leakage along the length of the uniform waveguide, where the dominant or above-cutoff higher mode itself is leaky. In addition, because of dimensional tolerance problems in the fabrication of open waveguides of small cross section, slight asymmetry can be introduced that causes a bound mode to leak. Examples are presented to illustrate each of the situations, although the limited space available does not permit the inclusion of analytical expressions for the leakage or numerical examples. Some interesting problems in electromagnetics arise in connection with some of these considerations.