Several rivers run through the commune: the Sâne Morte (especially to the eastern edge of Varennes), the Sevron and the Solnan (bordering Dommartin-lès-Cuiseaux then Frontenaud).

In 1790, Buisserolles (or Busserolles), which is today a hamlet of Varennes, was at that time an independent commune attached to the Ain department and to the township of Saint-Trivier-de-Courtes, which numbered 843 inhabitants according to the 1793 census.

Claude Alexis Yoland de Saint-Mauris Royalist January 1970 March 2001 René Beaumont UMP Veterinarian, former deputy, senator and president of the general council of Saône-et-Loire March 2001 to the present Jean-Michel Longin Responsable de bases The change in the number of inhabitants has been found through the censuses of the population taken in the commune since 1793.

Bresse Dairy (la Bressane) : agricultural cooperative founded in 1939 which became a private enterprise in 1992, it was reorganized in 2010 and employs 90 employees (office and production) en 2014.

Brunehilde who took refuge for a time in Burgundy during the uprising of the powerful leaders of Austrasia, left the name of «La Reine» ["the Queen"] to an intersection of Varennes-Saint-Sauveur on Highway D 996 in the direction of Louhans.

Bernard Bourgeois, philosopher, expert in Kant and Hegel ; elected 2 December 2002 to the philosophy section of the Academy of moral and political sciences, to the chair of d'Olivier Lacombe.