Theories for the formation of plasma and dust voids (large-amplitude ion and dust holes) in a complex plasma with static and mobile negatively charged dust are presented. It is shown that a plasma (dust) void in a complex plasma with negatively charged static (mobile) dust can be formed due to the presence of negative (positive) plasma potential, which is built up owing to a non-isothermal ion (dust) distribution arising from ion (dust) trapping. The plasma voids shrink when the dust grains are added into the plasma, and they tend to disappear if the dust number density is sufficiently high. On the other hand, the dust voids shrink with an increase in the dust charge density, but enlarges with an increase in the dust temperature.