Exploration is one of the primordial ways to accrue knowledge about the world and its nature.

As we accumulate, mostly automatically, data at unprecedented volumes and speed, our datasets have become complex and hard to understand.

In this context, exploratory search and analysis provide a powerful tools for progressively gathering the necessary knowledge when dealing with new or unfamiliar datasets.

When dealing with complex data, we are in need of powerful data models that give us the necessary expressivity to properly handle the richness and intricacies of the data at hand.

The graph model in general and Knowledge graphs (KGs) in particular are quickly becoming the best data models in these cases.

KGs represent facts in the form of nodes linked by relationships and are widely used to represent and share knowledge in many different domains.

The widespread adoption of knowledge graphs led to the advent of new exploration approaches to better understand their contents and extract relevant insights.

This talk will provide an overview of such methods focusing especially on the exploratory techniques we recently developed, the advantages they offer, as well as on the abundant research challenges that we still need to overcome.