During the Edo period, only the most skilled swordsmen were chosen to test swords, so that the swordsman's skill was not a variable in how well the sword cut. The materials used to test swords varied greatly, but the generally preferred targets were condemned criminals and cadavers. The other substances were wara (rice straw), goza (the top layer of tatami mats), bamboo, and thin steel sheets.
In addition, there were a wide variety of cuts used on the cadavers, from tabi-gata (ankle cut) to O-kesa (diagonal cut from shoulder to opposite hip). The names of the types of cuts on cadavers show exactly where on the body the cut was made. Older swords can still be found today that have inscriptions on their nakago (tang) that say things such as, "5 bodies with Ryu Guruma (hip cut)".
Aside from specific cuts made on cadavers, there were the normal cuts of Japanese swordsmanship, i.e. downward diagonal (Kesa), upward diagonal (Kiri-age), horizontal (Yoko), and straight downward (Jodan-giri, Happonme, or Dotan). These cuts would then be cut on the cadavers (ex: A swordsman would do a Jodan-giri cut on 3 bodies at the hips. the inscription would then be, "3 bodies Ryu Guruma"). The easiest cut is the downward diagonal, followed by the upward diagonal, followed by the straight downward cut, and finally the hardest cut, the horizontal.
In modern times, the practice of tameshigiri has come to focus on testing the swordsman's abilities, rather than the sword's. The targets most often used at present is the goza or tatami "omote" rush mat and synthetic targets. To be able to cut consecutive times on one target, or to cut multiple targets while moving, requires that one be a very skilled swordsman. There are a number of exceptional swordsmen who have recently set records in this field of tameshigiri, such as Russell McCartney of Ishi Yama Ryu and Saruta Mitsuhiro of Battodo Ryu Sei Ken. Russell McCartney recently set a new world record when he broke the record for Senbongiri (Lit. "1,000 cuts") with 1,181 consecutive cuts on igusa goza mat in 1 hour and 25 minutes. Saruta Mitsuhiro holds the record for Kabuto Wari, or helmet cutting, for his cut on a steel Kabuto (helmet).
Also, there are now specific cuts that can be performed on targets to test one's ability. An example is Mizu-Gaeshi, where one cuts a diagonal upward cut to the right and then cuts a horizontal cut on the cut piece before it has fallen.
Here at SwordsandWeapons.net, we offer the modern swordsman everything needed to begin cutting practice or continue tameshigiri training if you are already an experienced cutter.