Founded by Shirata Sensei, Classical Aikido is a style of the art which emphasises the philosophical teachings of Aikido, and is known for its vast, well-structured (but ever-changing) sets of techniques.
Shirata Sensei was a live-in student of Morihei Ueshiba O-Sensei for most of the Founder's teaching career, and the sets of techniques often follow the progression of O-Sensei's techniques throughout his life.
In the beginning, O-Sensei's techniques were like diamond - sharp, hard, and square to the four directions. The techniques then moved through willow and flow until, at the end of O-Sensei's life, they can only be described as ki throws. The diamond techniques are those taught to new students. Shiho nage is the quintessential example of these. Ki technique are reserved for those who have more experience.
Like many aspects of the style, the philosophy of Classical Aikido is well-organized. It is based around the Eight Pillars, and come from O-Sensei's teachings.
Today, Classical Aikido is led by John Stevens Sensei, a white guy. He has students around the world - in particular, Japan, Hawaii, the USA, Spain, Belgium, Holland, and Slovakia (to the best of my rememberance).