Trotskyism has become a by-word used by Stalinists to mean a traitor; in the Spanish Civil War, being called a "Trotskyist" or "Trotskyite" by the Communist supported elements implied that the person was a fascist spy or agent provocateur. George Orwell wrote about this in Homage to Catalonia and in his essay Spilling the Spanish Beans. Note: while both "Trotskyist" and "Trotskyite" are words that were probably originally coined by Stalinists to mark those who sided with Trotsky in factional disputes, "Trotskyist" is a term that is claimed by many, though not all, adherents of Trotsky's views. "Trotskyite" retains its pejorative connotation.
In 1938 Trotsky established the Fourth International. After his death this organisation has split many times. Trotskyist parties and groups are notorious for their tendency to split into smaller groups, quarrelling over theoretical differences that seem insignificant or indecipherable to an outsider.
Many developed countries have several different organizations which claim some tendency of Trotskyism. A few common exemplars include the Socialist Workers Party and the Socialist Party (formerly Militant) in Great Britain, Lutte Ouvrière and the Ligue communiste revolutionnaire in France, and the International Socialist Organization and the Spartacist League (see International Spartacist Tendency) in the United States.