Boston’s housing boom is spilling over into more corners of the city.

Two of the largest developments Dorchester has seen in a generation — nearly 900 apartments combined — won approval from city officials Thursday night.

So did a new apartment building in a stretch of Brighton that’s bubbling with new development. Smaller apartment and condo projects in Mission Hill, West Roxbury, and along Beacon Street near the Brookline border were OK’d, as well.

Taken together, the projects reflect a surge of development in neighborhoods beyond downtown and hot stretches of South Boston, the South End, and the Fenway that have been the focus of development in recent years. And they have the potential to add housing — in some cases at lower costs — in neighborhoods where demand has fast outpaced supply.

“Our goal is to provide exceptionally high-quality housing at rents that are dramatically lower than downtown Boston,’’ said Bruce Percelay, chairman of Mount Vernon Group, which won approval for a 132-unit apartment building on Western Avenue in Brighton.

To be clear, the hot areas are still very hot.

The biggest project approved at a marathon session of the Boston Redevelopment Authority’s board Thursday was a three-building complex on Seaport Boulevard that would include 733 apartments and condos above retail space and a large underground parking garage.

At $864 million, it would be among the most expensive construction projects in Boston’s current building boom. Still, developers from Los Angeles-based Cottonwood Management said they’re confident there will be demand when the units start to open in three years, even at the lofty prices such an expensive building would probably need to command.

There’s relatively little for-sale housing being built in the Seaport, said Cottonwood principal Alex Shing. His project would include more than 400 condos.

“To make a neighborhood, you need residents. And you need people who will put down roots,’’ he said. “We see a lot of demand for ownership there.’’

Other developers are banking on more modestly priced housing in areas that are long-overlooked but hold a lot of potential.

That’s the idea, in part, behind Eden Properties’ plan for a 700,000-square-foot expansion of the South Bay Shopping Center on the northern edge of Dorchester. The 10-acre site would include restaurants, a hotel, and a movie theater, and 475 apartments on upper floors. The South Carolina company owns South Bay and sees enormous demand in the neighborhood for retail and the kind of high-quality housing that has sprung up in pricier ZIP codes.

“There’s just a void there,’’ said Brad Dumont, senior vice president of development. “There isn’t a lot in Dorchester in terms of retail and restaurants. And we’re going to bring a sophisticated residential product to an area that hasn’t seen as much of that.’’

The board approved the plan after heated comments from neighbors — some in favor of more retail, some concerned about the impact on traffic and real estate costs.

And about a mile and a half south, along Dorchester Avenue between Savin Hill and Fields Corner, another huge mixed-use complex known as DotBlock would add 362 apartments and retail, perhaps including a grocery store, to a busy intersection. The biggest project in years in the neighborhood, it also sits along a stretch of Dorchester Avenue and Freeport Street that the BRA plans to rezone for more dense, transit-oriented development.

It’s a smart place to launch a project that could help transform a neighborhood, said City Council member Frank Baker, who represents the area.

“We need to build on our density in our neighborhood,’’ he said. “I think this is going to be great for Dorchester, and great for the city.’’

Then there’s Brighton, where a big landlord, Mount Vernon Co., won approval for a 132-unit apartment building on the corner of Western Avenue and Birmingham Parkway. The project would be in a corridor near Harvard University’s Allston campus that has seen a noticeable uptick in development lately and about a quarter-mile from Boston Landing, the New Balance-anchored mixed-use project that’s bringing a new commuter rail station to the area.

It’s the sort of place where developers say they can build good rental housing at somewhat reasonable rents.

“Our goal is to provide luxury housing at rents that are 30 percent, maybe 40 percent, lower than downtown Boston,’’ said Mount Vernon’s chairman, Bruce Percelay.

Not all the project applications went smoothly.

Several West Roxbury residents showed up — some hoisting signs saying “Mallards before Millionaires’’ — to oppose a townhouse project near Allandale Woods that has become a flashpoint for concerns about development in the city’s southwestern-most neighborhood.

Board members had sharp questions about the project’s environmental impact.

One member, Ted Landsmark, even cast a relatively rare “no’’ vote. But his four colleagues voted to approve the project, which will go next to the Zoning Board of Appeals to consider needed changes in zoning in the area.

Neighbors say they’ll continue to press their case.

Another West Roxbury project, a 46-unit apartment building on Washington Street across from Stony Brook Reservation, passed.

The BRA also approved a 45-unit apartment building on Beacon Street across the Massachusetts Turnpike from Kenmore Square; a 33-unit apartment building on Tremont Street in Mission Hill; and a pair of condominium buildings in South Boston.

Tim Logan can be reached at timothy.logan@globe.com. Follow him on Twitter at @bytimlogan.