Hawaiian earrings and their r-dimensional generalizations, r >1, have recently attracted a lot of attention of algebraic topologists for several reasons. These are compact metric spaces which are locally nice everywhere except at one point, and consequently have quite complicated fundamental groups. Their homology groups and homotopy groups are yet not fully computed though several interesting partial results have been obtained. Barrat and Milnor were first to use these spaces to give an example of a space whose homology groups have no respect for the dimension of the space. They also left open several questions which are currently being tackled. The talk will highlight some of the recent results on these problems.