A novel approach for nanoscale imaging and characterization of the orientation dependence of electromechanical properties-vector piezoresponse force microscopy (Vector PFM)-is described. The relationship between local electromechanical response, polarization, piezoelectric constants, and crystallographic orientation is analyzed in detail. The image formation mechanism in vector PFM is discussed. Conditions for complete three-dimensional (3D) reconstruction of the electromechanical response vector and evaluation of the piezoelectric constants from PFM data are set forth. The developed approach can be applied to crystallographic orientation imaging in piezoelectric materials with a spatial resolution below 10 nm. Several approaches for data representation in 2D-PFM and 3D-PFM are presented. The potential of vector PFM for molecular orientation imaging in macroscopically disordered piezoelectric polymers and biological systems is discussed.