Lead zirconate titanate (Pb(Zr1-xTix)O3 or PZT) ferroelectric ceramics have been widely used in transducers, actuators, and sensors, since they posses high dielectric and piezoelectric properties with a relatively high temperature of operation. Commercially used PZT ceramics are always modified by different dopants and are divided into the "soft" (donor doped) and "hard" (acceptor doped) groups. Compared with the undoped composition, hard PZT often shows lower but more stable properties after ageing. In contrast, soft PZT shows higher properties and insensitivity to ageing. The difference in properties between the soft and hard PZT ceramics is rather large, even though the doping level is limited to a very low value (on the order of 1 mole %). The large difference of the physical properties between them mainly originates from the contributions from domain wall motion rather than properties of the crystal lattice. However, the mechanisms of hardening and softening are not well understood. In order to understand better the hardening and softening mechanisms, in this thesis the different contributions to the dielectric properties of soft and hard PZT ceramics are studied by means of a broadband dielectric spectroscopy from 10 mHz to 20 GHz. Properties at THz and infrared frequencies where only crystalline lattice contributes to the dielectric response were also investigated in collaboration with another group. In the frequency range below 20 GHz, the different contributions to the permittivity by domain wall motion were revealed in hard and soft materials. In order to correlate the properties to the microscopic structure of hard and soft PZT ceramics, the domain structures were also investigated by transmission electron microscopy. Piezoelectric spectroscopy was employed to help separating different contributions at frequencies below 100 Hz. The main results of this work are: The microwave dielectric dispersion of all PZT ceramics (including undoped, soft and hard PZT ceramics), which is characterized by a rapid decrease of the permittivity and a loss peak in the GHz frequency range, is contributed by both domain wall motion and piezoelectric grain resonances. These two mechanisms are separated by gradual poling of samples. The dispersion related to the domain wall motion appears at a higher frequency than the one related to grain resonance and constitutes the main contribution to the microwave dielectric properties of unpoled samples. Above the GHz frequency range, the dielectric properties of hard and soft PZT ceramics are rather close and approach the upper limit value of their intrinsic properties, which are identified by dielectric properties determined by THz dielectric spectrum. The contributions by domain wall motion make up more than 50% of the quasistatic dielectric properties (measured at 100 kHz) in all studied samples. Below GHz frequency range, another dielectric dispersion due to the domain wall creep, which manifests itself by a logarithmic decrease of permittivity with increasing frequency, is indentified in both soft and hard PZT ceramics in a relatively broad frequency region over at least eight decades. The difference of the dielectric properties between the hard and soft PZT mainly results from this logarithmic dispersion, since soft PZTs exhibit stronger logarithmic dispersion than hard PZTs. By controlling the doping kind and crystalline symmetry, the slope of the logarithmic function can be adjusted. Large values are observed in the system with disordered distribution of defect dipoles (soft, donor doped materials) while nearly zero slope could be observed in hard, acceptor doped materials with tetragonal structure with defect dipoles well aligned with polarization within domains. Rapid increase of both permittivity and loss below 1 Hz, which cannot be described by the logarithmic function, is observed in hard PZT ceramics. To interpret this behavior, results of dielectric spectroscopy were complemented by piezoelectric measurements in the frequency range from 10 mHz to 100 Hz. The absence of the strong dispersion in the piezoelectric properties and presence in the dielectric response strongly indicates that its origin is in charge transport (such as hopping conductivity) rather than in motion of domain walls. Nanodomains, observed in Fe3+-doped hard PZT with composition at morphotropic phase boundary do not lead to the high dielectric and piezoelectric properties, as would be expected from some theoretical models. Acceptor doping rapidly decreases the domain size in PZT ceramics with compositions in rhombohedral, tetragonal and MPB regions. This effect could not be interpreted by the decrease of the grain size according to the commonly assumed parabolic relationship between the domain size and grain size. The small domain size is rather related to the presence of oxygen vacancies which break continuity of polarization.