Tengu is a race prominently featured in 4Kids' cartoon series. However, several seemingly contradictory statements in the series serve to obscure the origins and membership of this species.
Tengu (天狗, literally meaning "heavenly dogs") are a race of divine demons in Japanese mythology. Like most species, they can be either good, or evil, or fall somewhere in between. The tengu have had a variety of different appearances over the centuries, including a skybound dog (hence, the name), a large bird-like creature, and more recently, human-like with large noses (and sometimes wings).
Many legends are attributed to tengu. They have been said to have lived as mountain sages and were the creators of Ninjutsu. They were masters of many forms of combat, especially armed combat, and were known for wielding, among other weapons, swords, naginata, and magical fans. There exist seventeen daitengu (大天狗), or great tengu, whose strength, knowledge, and power exceed all others of the species. The most powerful daitengu is named Sojobo.
Other than vague references such as the Sword of Tengu, Tengu are first mentioned in the episode The Ultimate Ninja. It is said that Ultimate Ninja and his father, the Ultimate Daimyo, belong to a race that inspired the earthly legend of the tengu, and like the real world legend, created what is known today as ninjutsu.
The origins of the tengu and ninjutsu are quite different in The Lost Episodes. Tengu seems to be used as a catch-all term in this season for a Japanese demon, bringing forth such creatures as the Nezumi-Tengu (rat tengu) and Kappa-Tengu (Kappa being a separate species of demon unto their own). The most prominent tengu, however, is the original being known as The Shredder, a gigantic demon that terrorized Japan hundreds of years ago. He was defeated by the Five Dragons, who in this season, were the ones said to have created ninjutsu. The final blow on the demonic Shredder was performed by Oroku Saki, who had made a deal with the devil to absorb his power upon destroying its mortal form.
In the prequel motion comic Teenage Mutant Ninja Turtles: Tales from the Turtle Lair, Splinter tells a story of how the warrior spirit Sojobo would send his tengu to face a bushi (warrior) before they were able to be called ninja. Splinter, as Hamato Yoshi, faced this tengu, as do the Turtles in the present. The Tengu that tests the Turtles is secretly Splinter in disguise.