Linear mixed models are widely used across many disciplines due to its flexibility to model many complex data. The flexibility includes taking into account a hierarchical or correlated structure and the consideration of the different sources of variability. These complex structures can give rise to many different variance parameters. The estimation of variance components can be negative under certain methods and these have long been baffling to practitioners. These cases are sometimes unnoticeable due to the software’s inherent restriction for variance components to remain positive. In such a case, it is often that the variance components are close to the zero boundary. The occurrence of negative variances is attributed to a range of reasons. We present examples, based on agricultural experiments, of the occurrences of negative estimates of variance components and the consequences of ignoring random effects with negative variance components with respect to the aim of the analysis.