The lunar phase depends on the Moon's position in orbit around the Earth, and the Earth's position in orbit around the sun. This diagram looks down on Earth from the north. Earth's rotation and the Moon's orbit are both counter-clockwise here. From this diagram, we can see, for example, that the full moon will always rise at sunset, and that the waning crescent moon is high overhead around 9:00 AM local time. Lunar phases are the result of our seeing the illuminated half of the Moon at different angles. The Moon exhibits different phases as the relative positions of the Sun, Earth and Moon change, appearing as the Full moon when the Sun and Moon are on opposite sides of the Earth, and becoming invisible as the New Moon (also named Dark Moon) when they are on the same side: these two phases are examples of syzygies. The time between two Full Moons (or between successive occurrences of any two phases - for examples, First Quarter Moon to the next First quarter Moon) is about 29.53 days (or 29 days, 12 hours, 44 minutes); it is longer than the time it takes the Moon to orbit the Earth since the Earth-Moon system is orbiting the Sun. The phases are not created by the shadow of the Earth on the Moon (that would be a lunar eclipse); instead, they are a result of our seeing only part of the illuminated half of the Moon. Dark Moon - Not visible
New Moon - Not visible, or traditionally: first visible crescent of the Moon Waxing Crescent Moon - Right 1-49% visible
First Quarter Moon - Right 50% visible
Waxing gibbous Moon - Right 51-99% visible
Full Moon - Fully visible
Waning gibbous Moon - Left 51-99% visible
Third Quarter Moon - Left 50% visible
Waning Crescent Moon - Left 1-49% visible
New Moon - Not visible
In the southern hemisphere, the above is reversed. For example: Waxing Crescent Moon - Left 1-49% visible
Waning Crescent Moon - Right 1-49% visible
When the Sun and Moon are on opposite sides of the Earth, the Moon appears full: the Moon appears as a wholly-illuminated disk. As the Moon orbits Earth, the Moon wanes, as the amount of illuminated lunar surface reduces, until the Moon effectively disappears at the New Moon, when the Moon is between Earth and the Sun and thus the illuminated half cannot be seen at all.
Gibbous (red) and crescent (blue) shapes resulting from dividing a circle with an inscribed half-ellipse.
Animation of the Moon as it cycles through its phases. The apparent wobbling of the Moon is known as libration. According to geometry, when a sphere is illuminated on one hemisphere and viewed from an angle, then the portion of the illuminated area visible from that angle will be observed to have the two-dimensional shape of a half-ellipse inscribed within a half-circle, where the major axis of the ellipse is the same as the diameter of the semicircular arc. If the half-ellipse is convex with respect to the half-circle, then the shape will be gibbous, and if the half-ellipse is concave with respect to the half-circle, then the shape will be a crescent. If the eccentricity of the ellipse is 1, then a half-circle will be seen; while if the eccentricity of the ellipse is 0, then either a fully-illuminated or fully-dark circular disk will be seen (i.e. a full moon or new moon). Of course, actual observations of the Moon's lit area will not completely correspond with these abstract geometrical shapes, due to varying surface reflectivities, the lesser brightness of illuminated areas which are viewed at a low angle, etc. The different phases of the Moon...