The minimum variance (MV) beamformer has the potential to enhance the resolution and contrast of ultrasound images but is sensitive to steering vector errors. Robust MV beamformers have been proposed but mainly evaluated in the presence of gross sound speed mismatches, and the impact of phase aberration correction (PAC) methods in mitigating the effects of phase aberration in MV beamformed images has not been explored. In this study, an analysis of the effects of aberration on conventional MV and eigenspace MV (ESMV) beamformers is carried out. In addition, the impact of three PAC algorithms on the performance of MV beamforming is analyzed. The different beamformers were tested on simulated data and on experimental data corrupted with electronic and tissue-based aberration. It is shown that all gains in performance of the MV beamformer with respect to delay-and-sum (DAS) are lost at high aberration strengths. For instance, with an electronic aberration of 60 ns, the lateral resolution of DAS degrades by 17% while MV degrades by 73% with respect to the images with no aberration. Moreover, although ESMV shows robustness at low aberration levels, its degradation at higher aberrations is approximately the same as that of regular MV. It is also shown that basic PAC methods improve the aberrated MV beamformer. For example, in the case of electronic aberration, multi-lag reduces degradation in lateral resolution from 73% to 28% and contrast loss from 85% to 25%. These enhancements allow the combination of MV and PAC to outperform DAS and PAC and ESMV in moderate and strong aberrations. We conclude that the effect of aberration on the MV beamformer is stronger than previously reported in the literature and that PAC is needed to improve its clinical potential.