Many of the reddest stars in the sky, such as Y CVn, V Aql, and VX Sgr are LPVs. Most LPVs, including all Mira variables, are thermally-pulsing asymptotic giant branch stars with luminosities several thousand times the sun. Some semiregular and irregular variables are less luminous giant stars, while others are more luminous supergiants including some of the largest known stars such as VY CMa. Between a quarter and a half of long period variables show very slow variations with an amplitude up to one magnitude at visual wavelengths, and a period around ten times the primary pulsation period. These are called long secondary periods. The causes of the long secondary periods are unknown. Binary interactions, dust formation, rotation, or non-radial oscillations have all been proposed as causes, but all have problems explaining the observations. Mira variables are mostly fundamental mode pulsators, while the semiregular and irregular variables on the asymptotic giant branch pulsate in the first, second, or third overtone. Many of the less regular LPVs pulsate in more than one mode. Long secondary periods cannot be caused by fundamental mode radial pulsations or their harmonics, but strange mode pulsations are one possible explanation.