This seminar investigates the main similarities and discrepancies among three important current decompositions proposed for the consideration of unbalanced and/or nonlinearthree-phase three-wire power circuits. The considered approaches were the so called FBD Theory, the pq-Theory and the Conservative Power Theory (CPT), recently presented by Tentiet al.. Such decompositions and related definitions may influence the power measurement techniques, revenue metering, instrumentation technology and also power conditioning strategies. The three methods have been summarized, discussed and compared by means of computational simulation. Although the three methods are based on different concepts, the results obtained under ideal conditions are very similar. The main differences appear in the presence of unbalanced and non linear load conditions. Under linear unbalanced conditions, both FBD and pq-Theory suggest that the some current components contain a third-order harmonic. Besides, neither pq-Theory nor FBD method are able to provide accurate information for reactive current under unbalanced and distorted conditions, what can be done by means of the CPT-Theory. The paper tries to explain the causes of these differences in terms of the decomposition's foundations and the resulting waveforms and spectra.