We present systematic investigations on the physics, detection performance and inversion of logging-while-drilling extra-deep azimuthal resistivity measurements (EDARM). First, the definitions of EDRAM measurements are discussed, followed by the derivation of the attenuation and phase-shift geometrical factors to illustrate the relative contributions of formation units to the observed signals. Then, a new definition of detection depth, which considers the uncertainty of inversion results caused by the data noise, is proposed to quantify the detection capability of EDARM. Finally, the Bayesian theory associated with Markov chain Monte Carlo sampling is introduced for fast processing of EDARM data. Numerical results show that EDARM is capable of detecting the azimuth and distance of remote bed boundaries, and the detection capability increases with increasing spacing and resistivity contrast. The EDARM tool can accommodate a large range of formation resistivity and is able to provide the resistivity anisotropy at arbitrary relative dipping angles. In addition, multiple bed boundaries and reservoir images near the borehole are readily obtained by using the Bayesian inversion.