In the decades since the discovery of radar, scientists have discovered new ways to harness additional parts of the electromagnetic spectrum to replicate radar in new ways. From back scattered x-rays used in airports, to green lasers used to measure distances to the moon, we now have a whole arsenal of technologies with which to explore our Solar System. The most commonly used modern technology is laser ranging. This technique is completely analogous to radar ranging, but because laser light has much smaller wavelengths, laser measurements can be much more accurate.
From the surface of the Earth, astronomers regularly laser range the moon and artificial satellites to get accurate distances and velocities across the sky (and to thus calculate orbits, which in the case of satellites, others may not wish one to know.) This technique, which employs green or other visible light lasers, allows us to calculate the distance of the moon with millimeter accuracy.
Lasers are also used on orbiting space probes. These LIDAR (for Laser I-mage Detection and Ranging) Systems have used since the Clementine mission to the moon to make high resolution measurements of planetary surfaces. Like with radar images, the characteristics of the laser return — the reflected laser beam — gives insight into the planet's surface texture and composition. The original Clementine LIDAR was able to measure the height (and depth) of lunar structures with an accuracy of 40 meters. The Lunar Reconnaissance Orbiter's system, called LOLA (for Lunar Orbiter Laser Altimeter) improves on this several fold, making maps of the Lunar surface with accuracies within 10 cm in height and over a 30 cm diameter.
LIDAR maps instruments have been placed in orbit of the Moon and Mars, and the MESSENGER mission brings us novel measurements of Mercury. Combined with images, these altimetry measurements provide new insights into different planetary structures. The combination of texture and depth from LIDAR, and composition from spectral imaging (or at least multi-filter imaging) allows geologic features to be mapped in detail.