Substitutional charge disorder giving rise to quenched electric random-fields (RFs) is probably at the origin of the peculiar behavior of relaxor ferroelectrics, which are primarily characterized by their strong frequency dispersion of the dielectric response and by an apparent lack of macroscopic symmetry breaking at the phase transition. Spatial fluctuations of the RFs correlate the dipolar fluctuations and give rise to polar nanoregions in the paraelectric regime as has been evidenced by piezoresponse force microscopy (PFM) at the nanoscale. The dimension of the order parameter decides upon whether the ferroelectric phase transition is destroyed (e.g. in cubic PbMg1/3Nb2/3O3, PMN) or modified towards RF lsing model behavior (e.g. in tetragonal Sr1-xBaxNb2O6. SBN, x approximate to 0.4). Frustrated interaction between the polar nanoregions in cubic relaxors gives rise to cluster glass states as evidenced by strong pressure dependence, typical dipolar slowing-down and theoretically treated within a spherical random bond-RF model. On the other hand, freezing into a domain state takes place in uniaxial relaxors. While at T-C non-classical critical behavior with critical exponents gamma approximate to 1.8, beta approximate to 0.1 and alpha approximate to 0 is encountered in accordance with the RF lsing model, below T-C approximate to 350 K RF pinning of the walls of frozen-in nanodomains gives rise to non-Debye dielectric response. It is relaxation- and creep-like at radio and very low frequencies, respectively. (c) 2006 Springer Science + Business Media, Inc.