Geometries and bond dissociation energies of the ylide compounds H2CPH3, H2CPMe3, H2CPF3, (BH2)2CPH3, H2CNH3, H2CAsH3, H2SiPH3, and (BH2)2SiPH3 have been calculated using ab initio (MP2, CBS-QB3) and DFT (B3LYP, BP86) methods. The nature of the ylidic bond R2E1-E2X3 was investigated with an energy decomposition analysis and with the domain-averaged Fermi hole (DAFH) analysis. The results of the latter method indicate that the peculiar features of the ylidic bond can be understood in terms of donor-acceptor interactions between closed-shell R2E1 and E2X3 fragments. The DAFH analysis clearly shows that there are two bonding contributions to the ylidic bond. The strength of the donor and acceptor contributions to the attractive orbital interactions can be estimated from the energy decomposition analysis (EDA) calculations, which give also the contributions of the electrostatic attraction and the Pauli repulsion of the chemical bonding. The EDA and DAFH results clearly show that the orbital interactions take place through the singlet ground state of the R2E1 fragment where the donor orbital of E1 yields pi-type back-donation while the E2X3 lone-pair orbital yields sigma-type bonding. Both bonds are polarized toward E2X3 when E2 = P, while the sigma-type bonding remains more polarized at E2X3 when E2 = N, As. This shows that the phosphorus ylides exhibit a particular bonding situation which is clearly different from that of the nitrogen and arsenic homologues. With ylides built around a P-C linkage, the pi-acceptor strength of phosphorus and the sigma-acceptor strength at carbon contribute to a double bond which is enhanced by electrostatic contributions. The strength of the sigma and pi components and the electrostatic attraction are then fine-tuned by the substituents at C and P, which yields a peculiar type of carbon-phosphorus bonding. The EDA data reveal that the relative strength of the ylidic bond may be determined not only by the R2E1 --> E2X3 pi back-donation, but also by the electrostatic contribution to the bonding. The calculations of the R2E1-E2X3 bond dissociation energy using ab initio methods predict that the order of the bond strength is H2C-PMe3 > H2C-PF3 > H2C-PH3 > (BH2)2C-PH3 > H2C-AsH3 > H2C-NH3 approximately H2Si-PH3 approximately (BH2)2Si-PH3. The DFT methods predict a similar trend, but they underestimate the bond strength of (BH2)2CPH3.