What sports and martial arts comprise fencing?

The Olympic sport of fencing is comprised of three weapons:  foil,
epee, and sabre.  The rules governing these three weapons are
determined by the FIE (Federation Internationale d'Escrime).
Briefly, the FIE weapons are described as follows:

Foil:  Descended from 18th century court sword training weapons.  The
       foil has a thin, flexible blade with a square cross-section and a
       small bell guard.  Touches are scored with the point on the torso
       of the opponent, including the groin and back.  Foil technique
       emphasizes strong defense and the killing attack to the body.

Epee:  Similar to the duelling swords of the mid-19th century,
       epees have stiff blades with a triangular cross section,
       and large bell guards.  Touches are scored with the point,
       anywhere on the opponent's body.  Unlike foil and sabre, there
       no rules of right-of-way to decide which attacks have precedence,
       and double hits are possible.  Epee technique emphasises timing,
       point control, and a good counter-attack.

Sabre:  Descended from cavalry swords of the late 19th century,
        sabres have a light, flat blade and a knuckle guard.  Touches
        can be scored with either the point or the edge of the blade,
        anywhere above the opponent's waist.  Sabre technique emphasises
        speed, feints, and strong offense.

The most popular of eastern fencing techniques is kendo, the Japanese
"Way of the Sword".  Kendo is fought with a bamboo shinai, intended
to resemble a two-handed Japanese battle sword.  Combatants wear
armour, and strike to the top or sides of the head, the sides of the
body, the throat, or the wrists.  Accepted technique must be
observed, and judges watch for accuracy, power, and spirit.  See the
Japanese Sword Arts FAQ for more information.

Other martial arts that include elements of swordsmanship are:

Aikido -- self defence against armed and unarmed attackers.  Includes
        using and defending oneself against Japanese sword techniques.
Arnis, Escrima -- stick fighting.
Iaido -- the Japanese art of the draw.
Kenjutsu -- the unadulterated Japanese martial art of the sword.
Iaido -- the Japanese art of the draw.
Kenjutsu -- the unadulterated Japanese martial art of the sword.
Kung-fu -- a Chinese martial art that includes many sword techniques.
Modern Pentathlon -- the "soldier's medley", a sport that recreates
       demands placed on a pre-20th century military messenger:  running,
       swimming, shooting, equestrian jumping, and epee fencing.
Single Stick -- an ancestor of sabre fencing.
SCA -- the "Society for Creative Anachronism", an organization that
        attempts to re-create the lifestyle of Medieval Europe, including
        jousts and tourneys.  Emphasizes heavy weapon and shield
        techniques, the use of armour, Florentine fencing, and fencing
        in the round.  Additional info on the SCA can be found in the
        newsgroup rec.org.sca.
Link to the next chapter: Which is the best weapon?