In 1974 Gromoll and Meyer found an example of an exotic 7-sphere, $\Sigma^7$, which can be described as a biquotient of a compact Lie group and hence admits a metric of non-negative curvature. This was the first exotic sphere to be shown to admit such a metric. Moreover, they showed that there is a point in $\Sigma^7$ at which all sectional curvatures are positive, and claimed that such a property held on an open dense set of points. It was later shown that this claim was, in fact, false. However, it is possible to deform the metric in such a way that the claim holds. We will give a summary of the interesting history of the Gromoll-Meyer sphere and how it remains central to research in non-negative and positive curvature, and illustrate how one equips it with a metric for which our claim above holds.