The limestone on which Odesa stands is riddled with some 2000km of tunnels, which have always played an important part in the city's history. Quarried out for building in the 19th century, they were first used to hide smuggled goods. During WWII they sheltered a group of local partisans who waged a war of attrition against the occupying Romanians and forced the Nazis to keep greater troop numbers in the area.
Most of the catacomb network lies well outside Odesa's city centre. The only tunnels that can be visited are in the suburb of Nerubayske, about 15km north of central Odesa. Here, a resident speleologist offers 45-minute catacomb tours that wend through what was the headquarters of Odesa's WWII partisan movement. Tours are in Russian, so you may wish to bring a translator along, although you don't necessarily need a translator to enjoy the catacombs. Tours exit into the musty Partisan Museum (accessible only via a tour).
Marshrutka 84 to Nerubayske leaves every 10 minutes from Odesa's Privoz bus station (35 minutes). Ask the driver to let you off at the 'Katakomby' stop, easily identifiable by the hulking Soviet realist statue depicting five defiant partisans. Tour agencies in Odesa run tours out here for about 1200uah per group.