Radio astronomy is known for its very large telescope dishes but is currently making a transition towards the use of a large number of small antennas. For example, the Low Frequency Array, commissioned in 2010, uses about 50 stations each consisting of 96 low band antennas and 768 or 1536 high band antennas. The low-frequency receiving system for the future Square Kilometre Array is envisaged to initially consist of over 131,000 receiving elements and to be expanded later. These instruments pose interesting array signal processing challenges. To present some aspects, we start by describing how the measured correlation data is traditionally converted into an image, and translate this into an array signal processing framework. This paves the way to describe self-calibration and image reconstruction as estimation problems. Self-calibration of the instrument is required to handle instrumental effects such as the unknown, possibly direction dependent, response of the receiving elements, as well a unknown propagation conditions through the Earth’s troposphere and ionosphere. Array signal processing techniques seem well suited to handle these challenges. Interestingly, image reconstruction, calibration and interference mitigation are often intertwined in radio astronomy, turning this into an area with very challenging signal processing problems.