Paraguay's flag is three horizontal stripes, red over white over blue, and it is the only national flag in the world that shows you something different depending on which side you are standing on.
Independence and the 1842 design
Paraguay broke from Spanish rule in 1811, and its early flags shifted with the politics of the period, caught between rejecting colonial symbols and settling on something of its own. A red, white, and blue tricolor was in use from 1812. José Gaspar Rodríguez de Francia, the dominant figure of Paraguay's first decades as an independent country, set it aside in 1826 in favor of a plain blue flag, and that is what flew until his death in 1840.
The tricolor came back after him. An extraordinary congress adopted the present design on November 25, 1842, under the consuls Carlos Antonio López and Mariano Roque Alonso, and it has survived every government since, democratic and otherwise, without losing its basic structure.
Two sides, two emblems
The obverse carries the national coat of arms: a yellow star inside two circular lines, wreathed by an olive branch and a palm branch, for peace and honor.
Turn the flag over and you get the treasury seal instead, with a lion and a Phrygian cap, for courage and liberty.
Red is bravery and patriotism, white is peace and purity, blue is liberty. The palette comes from the French tricolor, and so do the associations attached to it.
Plenty of Latin American countries use a tricolor, for the same reason: the same wave of revolutions, the same French and American models. The two-sided arrangement is what makes Paraguay's stand out on the continent.
Where it flies
The flag is flown on government buildings and at national events, Independence Day and Flag Day above all, with rules covering indoor and outdoor display. It appears in military ceremonies. There is also a civil ensign and a naval jack, which keep the national colors but follow maritime convention in their layout.
References
[1] Paraguayan Government Publications: History and Use of National Symbols.
[2] International Federation of Vexillological Associations: Flag Information.
[3] Historical Archives of Paraguay: Evolution of the National Flag.