We present detailed measurements of the electrical resistivity and microcalorimetry under magnetic field and high pressure which confirm the proximity of YbRh₂Si₂ to a quantum critical point at ambient pressure. Our data seems to rule out the divergence of the heavy quasiparticle mass at the magnetic field tuned quantum critical point. Further Mössbauer spectroscopy gives evidence that the observed ESR resonance cannot be assigned directly to the trivalent Yb local spin dynamics. We report for the first time on quantum oscillations in YbRh₂Si₂. The obtained angular dependence is compared with band-structure calculation. A significant change of the resistivity and specific heat under high pressure and magnetic field is observed. Above 5 GPa ferromagnetic coupling plays the dominant role. The unusual high pressure phase diagram of YbRh ₂Si₂ cannot be explained in term of the Doniach phase diagram. In Yb heavy fermion case, slow valence fluctuations may occur due to an occupation number of the trivalent state which differs notably from unity. The differences between the Ce and Yb heavy fermion systems are discussed. In particular a comparison is made between CeRh₂Si₂ and YbRh₂Si₂. The observed field and pressure variations of the Hall voltage in CeRh₂Si₂ are not straightforwardly linked to the change in the Fermi surface topology. A tiny change in the 4f electron occupation number will have a huge effect on the effective mass of different orbits of the complex band structure and thus on the Hall effect in this multiband electronic structure. A similar scenario must be certainly considered for YbRh₂Si₂.