Abstract: The link of a complex isolated singularities is the odd-dimensional real manifold cut out by a sphere of radius arbitrarily small centred at that point. It plays a significant role in the description of the topology of a neighbourhood of the singularity. Unluckily, even basic invariants, like its fundamental group, are not fully understood.
In this expository talk I will provide some motivational examples without particular algebro-geometric prerequisites.
You can find a funny 3-minute introduction to the subject at https://www.youtube.com/watch?v=TpB9pa3j0l0.