The visibility of the thin crescent Moon is an important problem for t
he calendars of many societies, both ancient and modern. With roughly
1 x 10(9) people of the Islamic faith following the Islamic calendar,
this problem is likely to be the one (nontrivial) problem in astronomy
that has the greatest impact on our modern world. In the past decade,
great advances have been made in the observation and theory of cresce
nt visibility. This paper reports recent observations and analyses. Ne
w records have been set for the youngest Moon, with confident sighting
s at 15.0 hr by John Pierce with unaided vision and at 12.1 hr by Jim
Stamm with telescopic assistance. These records can be significantly b
roken under optimal conditions. Various prediction algorithms are test
ed with the 294 collected individual observations plus the 1490 observ
ations from the five Moonwatches. The age and moonset-lag criteria are
found to be poor, the altitude/azimuth criteria can make a confident
prediction only one-quarter of the time, while the best predictor by f
ar is the modern theoretical algorithm.