11.25 miles ; south from I-10 to US 90 west of New Orleans. This award-winning freeway was completed May 7, 1993. The Luling - Destrehan cable-stayed bridge, aka the Hale Boggs Memorial Bridge, is the first one of that type to cross the Mississippi River. The $135 million bridge, which opened in 1983 and was judged "Exceptional" in the 1984 FHWA Design Awards report, predates the freeway, and merely connected opposing river roads for many years. The last section of I-310 to open, a two-mile twin-bridge roadway over environmentally sensitive wetlands, won the 1992 Build America award in the Highway Division category. 
Compare this popularity to Louisiana's other I-310, below.
Colin "Gremillions" reviews I-310: "Actually it is now a fairly useful freeway, it goes near a large neighborhood in Norco, a tourist area and business park on the river, and a nuclear plant across the river." Two thumbs up :-)
Stephen Gantry says: "Coming down the 1.5 mile long Mississippi River Bridge southbound, you can see for miles literally! There is a little sugarcane field immediately at the base of the bridge. Northbound, you can see New Orleans metro about 10-30 miles to the east. The I-310/US 61 stack interchange is probably the best stack in all of Louisiana. I think this stack is as good as anyone in Texas. The whole thing is elevated above the swamps! That is a stack that should be photographed. From mile markers 7-11, I-310 is at ground level. At the terminus with US 90 ([Future] I-49) there are huge ghost ramps, probably for the interchange with I-49, and there is a lot of free land they can use to build the interchange." 
... but it's in the way of a proposed airport.
St. Charles International Airport LLC is proposing a new international airport, covering 8,000 acres, in St. Charles Parish wetlands near I-10 and stradding I-310. Plans include a taxiway over I-310, or even a relocation of I-310.  
510 - 310 connection to be revived?
Decades ago, Louisiana proposed an I-410, a 48-mile freeway connecting I-310 and I-510, bypassing New Orleans to the south. This was cancelled. However, in 2003 Louisiana's list of proposed "Megaprojects" included a new 43-mile freeway linking I-310 and I-510 ... in essence, reviving the 410 proposal. 
I-310 (cancelled) Louisiana
New Orleans was the scene of one of the United States' highest-profile freeway battles. Plans for the Vieux Carré Expressway, an elevated riverfront highway passing through the French Quarter, date back to 1946, when the Louisiana Highway Department was looking for solutions to New Orleans' traffic problems. The consultant they brought on board: Robert Moses, who had been building expressways in New York for over 20 years.
Not one to tinker with a working formula, Moses proposed several freeways for the area, including what would be called I-310. The route:
Debating a new interstate
By 1960, the Interstate Highway program had changed the funding equation for express highways, and interstate status was being considered for the Vieux Carré Expressway, also being called the Riverside or Riverfront Expressway. The route considered
Two questions were brought up: 
As for question 2, officials first looked at eliminating I-610, the so-called Florida Avenue cross connection that would enable I-10 drivers to avoid the city center. It was judged that I-610 was too useful, and that Interstate 12, which bypasses the metropolitan area altogether, still would not measurably decrease the need for I-610. 
Another approach was to adjust the southeastern leg of I-10 (that part of the triangle it forms with I-610) eastward to follow the riverside route, eliminating the need for extra mileage. 
In 1964, a state engineer arrived at the idea Lousiana went forward with later that year. I-610 would be preserved, and I-10 would not have to move. Adding the Vieux Carré Expressway as an interstate would come at the expense of a smaller city upstate.
Sorry, Monroe; I-310 in, I-420 out
Interstate 420, a proposed 10.2-mile northern bypass of Monroe, would be cashed in to free up system mileage. I-420's benefit, even in the scope of relieving I-20 traffic through the city, would not compare to how the Vieux Carré Expressway was expected to smooth traffic flow in New Orleans.
Though the Louisiana Highway Department had been considering a terminus at Lafayette Street for the new freeway, deleting I-420 would free up enough system miles and state funds to provide a connection to the Pontchartrain Expressway (BR US 90).
Second District congressman Hale Boggs championed the cause in Washington. On Oct. 12, 1964, he announced that the BPR had agreed to delete I-420. On Oct. 13, 1964, he announced that the Vieux Carre expressway was now officially Interstate 310.   The cost was $29 million, of which the federal government would contribute 90%.
This announcement, and the start of construction in a tunnel under the planned Rivergate convention center, woke up opposition. They pointed to what the nearby elevated I-10 had done to the formerly oak-lined Claiborne Avenue neighborhood (business and middle-class flight from noise and fumes from a second-story freeway). While I-10 had displaced a mostly black community with little opposition, I-310 was up against the French Quarter and a controversy quickly becoming national in scope. A 1968 Newsweek article covered the topic, and oratories on the "uglification of America" were heard in Washington. 
Word also got out that the state was planning an extension of the Vieux Carre 5 miles upriver (west), connecting a planned Earhart Expressway; and all of New Orleans began to have a stake in the outcome. In summer 1969, new Secretary of Transportation John A. Volpe rescinded approval for I-310 citing a violation of the National Historic Preservation act. For the next two decades, supporters still tried to get the highway built. 
Tom Lewis' book (see Sources) devotes a full chapter to the I-310 battle. The book is better than most highway history books (most freeways he mentions are cited by number in the index) but it still leaves the reader hungry for more. Perhaps there's no avoiding that.