  Low-frequency radio astronomy is limited by severe ionospheric distortions
below 50 MHz and complete reflection of radio waves below 10-30 MHz. Shielding
of man-made interference from long-range radio broadcasts, strong natural radio
emission from the Earth's aurora, and the need for setting up a large
distributed antenna array make the lunar far side a supreme location for a
low-frequency radio array. A number of new scientific drivers for such an
array, such as the study of the dark ages and epoch of reionization,
exoplanets, and ultra-high energy cosmic rays, have emerged and need to be
studied in greater detail. Here we review the scientific potential and
requirements of these and other new scientific drivers and discuss the
constraints for various lunar surface arrays. In particular we describe
observability constraints imposed by the interstellar and interplanetary
medium, calculate the achievable resolution, sensitivity, and confusion limit
of a dipole array using general scaling laws, and apply them to various
scientific questions. Whichever science is deemed most important, pathfinder
arrays are needed to test the feasibility of these experiments in the not too
distant future. Lunar low-frequency arrays are thus a timely option to
consider, offering the potential for significant new insights into a wide range
of today's crucial scientific topics. This would open up one of the last
unexplored frequency domains in the electromagnetic spectrum.
