Rapiers evolved from cut-and-thrust military swords, but were most
popular amongst civilians who used it for self-defence and duelling.
Rapiers were edged, but the primary means of attack was the
thrust. Rapier fencing spread from Spain and Italy to northwest
Europe, in spite of the objections of masters such as George Silver who
preferred traditional cutting weapons such the English broad sword.
The Spanish school, under masters such as Narvaez and Thibault,
became a complicated and mystical affair whose geometrical theories
required much practice to master. Italian masters like Agrippa
and Capo Ferro 
developed a more pragmatic school in the late 16th and
early 17th centuries, introducing innovations such as linear fencing
and the lunge.
By the 18th century, the rapier had evolved to a simpler, shorter,
and lighter design that was popularized in France as the small sword.
Although the small sword often had an edge, it was only to
discourage the opponent from grabbing the blade, and the weapon was
used exclusively for thrusting. The light weight made a more complex
and defensive style possible, and the French masters developed a school
based on defence with the sword, subtlety of movement, and complex
attacks. When buttoned with a leather safety tip that resembled a
flower bud, the small sword was known as le fleuret, and was identical
in use to the modern foil (still known as le fleuret in French).
Indeed, the French small sword school forms the basis of most of
modern fencing theory.
By the mid-19th century, duelling was in decline as a means of
settling disputes, partially because victory could lead to a jail term
for assault or manslaughter. Emphasis shifted to defeating the
opponent without necessarily killing him, and less fatal duelling forms
evolved using the duelling sword, or épée de terrain, an unedged
variant of the small sword. Later duels often ended with
crippling thrusts to the arm or leg, and fewer legal difficulties for
the participants. This is the basis of modern épée fencing.
Duelling faded away after the First World War. A couple of
noteworthy duels were fought over disputes that arose during Olympic
games in the 1920s, and there have been rare reports of sword duels
since then. German fraternity duelling (mensur) still occurs with
some frequency.
The first modern Olympic games featured foil and sabre fencing for
men only. Epee was introduced in 1900. Single stick was
featured in the 1904 games. Epee was electrified in the 1936
games, foil in 1956, and sabre in 1988. Early Olympic games
featured events for Masters, and until recently fencing was the only
Olympic sport that has included professionals. 
Disruptions in
prevailing styles have accompanied the introduction of electric
judging, most recently transforming sabre fencing. Foil fencing
experienced similar upheavals for a decade or two following the
introduction of electric judging, which was further complicated by the
new, aggressive, athletic style coming out of eastern Europe at the
time.