The experimental approach combining high resolution transmission electron microscopy (HRTEM), electron diffraction (ED) and resonant Raman spectroscopy (RRS) on the same freestanding individual carbon nanotubes (CNT) is the most efficient method to determine unambiguously the intrinsic features of the Raman-active phonons. In this paper, we review the main results obtained by the approach regarding the intrinsic features of the phonons of singlewalled (SWNT) and double-walled carbon nanotubes (DWNT). First, we detail the different methods to identify the structure of SWNTs and DWNTs from the analysis of their electron diffraction patterns (EDP). In the following, we remind the principal features of the Raman response of SWNTs, unambiguously index-identified by ED. A special attention is devoted to the effect of the inter-layer interaction on the frequencies of the Raman-active phonons in indexidentified DWNTs. The information obtained on index-identified SWNT and DWNT allows us to propose Raman criteria, which help identifying CNT when the ED fails to propose a single assignment. The efficiency of the Raman criteria as the complement to the ED information for the index-assignment of a few SWNTs and DWNTs is shown. The same approach to index-assign a triple-walled carbon nanotube (TWNT), by combining ED and RRS information, is reported.