Variance components and functions thereof are important in many fields such as industry, agriculture, quantitative genetics and animal breeding. This paper contributes to evaluating the variance components estimation approaches and assessing their robustness to outliers. Using an intensive simulation study and under different settings, it was found that researchers can decide which method of estimation is appropriate to their study to estimate the variance components based on the source of outliers (error term, εi j or random effects, αi), the variance components ratio, and the sample size.