One of the most popular and well-known clustering methods is K-Means clustering. It's conceptually simple. It's also easy to implement and is computationally cheap. We can get decent results quickly for many different datasets.
On the downside, it sometimes gets stuck in local optima and misses a better solution.
Generally, K-Means clustering performs best when groups in the data are spatially distinct and are grouped into separate circles. If the clusters are all mixed, this won't be able to distinguish them. This means that if the natural groups in the data overlap, the clusters that K-Means generates will not properly distinguish the natural groups in the data.