Täby is famous for its racecourse, which is called "Täby Galopp". The course opened in 1960 and it replaced the earlier course Ulriksdal in Solna. The Center of Täby is called "Täby centrum", and it is the largest mall in Sweden.
The name Täby is derived from tä, which is an old word that was used for "narrow road between roundpole fences", and by which means village. It is therefore believed that the Täby area was rich in such roads in the Viking age. The name Täby is found carved into the Jarlabanke Runestones, close to Täby church.
Täby has been inhabited since the Bronze Age. Around the Viking Age, the Täby area, as well as many other areas in the province of Uppland, developed into an agricultural area, which it largely remained until the early 20th century. In 1885 Täby got its first commercial shop, and in the same year the narrow-gauge regional railroad Roslagsbanan was opened, which gave the area much improved communications both to Stockholm and to the Roslagen area. From 1950 Täby has been an expansive suburban area of Stockholm.