In recent years there has been a growing interest from the industry for exploration in the Arctic and other high-latitude areas, including possible future petroleum provinces in Greenland. Exploration focus in Greenland has mainly been on central west Greenland with several licensing rounds and, as a promising result, the highest number of licences ever seen in Greenland. Activities in the coming years are likely to be directed more towards Baffin Bay and to the NE Greenland shelf. Both of these regions offer very promising exploration targets but also major technical challenges due to many months of ice coverage every year. Preparations for new exploration, data acquisition and geological and geophysical work are in progress in these two regions. Both of the regions benefit from excellent outcrops in the neighbouring onshore areas and a rapidly increasing geophysical database offshore. The history behind data acquisition and the most important results and models for exploration in some of the possible future petroleum provinces are described with particular focus on positive indications for structures and petroleum systems together with uncertainties in interpretation and the most critical risks for exploration.