Upzoning, in present usage, means changing the zoning of a land area to more intensive, mixed, and/or higher-density use. For example, from "single-family" zoning allowing just one unit per land lot, to a designation allowing a 4-unit building on the same lot.
In earlier times, especially prior to 1970, "upzoning" commonly meant the opposite: rezoning land to more restrictive and particularly residential uses. Fischel  suggests that this came from the metaphor of the land-use pyramid, with restricted residential use at the top of the pyramid of uses.
"in 1999, Houston enacted sweeping land-use reforms: it decreased the minimum residential lot size from 5,000 square feet to 1,400 in close-in neighborhoods. In effect, this reform legalized townhouses in areas with suburban-style houses on huge lots. Two or three houses could now take the spot of one.
"The political significance of these reforms cannot be overstated. Single family zoning is somewhat of a third rail in American local politics; it’s exceptionally rare for residents of suburban-style neighborhoods to allow denser development. Urbanist commentators have noted that “missing middle” housing — forms like duplexes and small multifamily apartments — has been regulated away in most American cities. Houston represents an important dissent from the notion that single family neighborhoods are to be preserved at all costs.
"The results of these reforms have been remarkable. Areas that were once made up entirely of ranch-style houses, McMansions, and underused lots are now covered in townhouses."
- [Ricci 2016].
Seattle Mayor Ed Murray has put forward plans (2017) for upzoning (in this context, allowing for taller and larger buildings) in certain designated zones in the city's downtown, South Lake Union and University districts as part of his Mandatory Housing Affordability (MHA) program. The taller, larger buildings (and connected tear-downs) would be allowed for areas supported by good transit and designated as "urban centers" and "urban villages." It would not touch single-family neighborhoods. The upzoning would go hand in hand with rent-regulated units being included in the new developments or developers' fees paid towards building affordable housing.
In Austin, Texas the conversation around "upzoning," particularly for opponents of the CodeNEXT land development codes of residential structures and developments that could take place while maintaining a "standard neighborhood look."
New York City
With plans for a Metro-North station on the horizon for Parkchester, Bronx (2017), Bronx Borough President Ruben Diaz, Jr. has spoken of "upzoning" Parkchester and two other Bronx neighborhoods slated for train stations.
“I think that we would be remiss if we didn’t look at the area as a potential way where we can increase density, residential units as well as commercial and real estate spaces. These areas are just ripe for that,” Diaz said.
The tenure of Mayor Michael Bloomberg (2002-2013) saw a lot of upzoning in New York City. That has continued under Mayor Bill DeBlasio (took office in 2014) who has also put a focus on affordable housing requirements and inclusionary zoning.
San Francisco 
In May 2017, YIMBY Action (San Francisco) issued a call to form a working group for upzoning single-family housing areas of the city. [YIMBY Action 2017]. Excerpts from the public letter:
"It is time to up-zone all single family and duplex lots to allow for more multifamily housing in every neighborhood in San Francisco.
For too long low-income and historically minority neighborhoods have been asked to shoulder a disproportionate amount of our city-wide housing needs. That injustice must end. It is time to build housing in every neighborhood.
The city is already largely zoned for a minimum of 4 stories. Up-zoning to allow 4 units would only acknowledge the truth: 4 housing units can be safely in almost every lot in the city - but if we only legalize multifamily housing. Our current low-density zoning incentivizes homeowners to add square footage (i.e. “Monster Homes”) without adding additional housing units. It enshrines a culture of protectionism and freezes wealthier neighborhoods in amber. Meanwhile, the city is breaking under the weight of a chronic housing shortage. This must end.
"The only way to solve the crisis is to create a continuous supply glut. About one third of our metropolitan area is zoned single family homes only (RH1 and RH1-
D). When you add in duplexes (RH2) and triplexes (RH3), we estimate 75% of the housing stock is artificially restricted to low density. These zoning policies are the
legacy of suburban sprawl, racist redlining, and misplaced fears of the “inner city”. The large demand for housing in these areas is reflected in the extremely high price
of housing in these neighborhoods."
"Up-zoning all lots to a minimum of RH-4 multifamily housing would ignite a housing development boom. It would legalize hundreds of thousands of units that are not possible today. These potential mid-rise housing developments would be in very desirable neighborhoods and are very feasible economically. Adding mid-rise multifamily housing in these neighborhoods would encourage a mixing of socio-economic backgrounds, enriching and diversifying our communities. These small-scale projects would be distributed throughout the city, bringing new life into every community. There are many smaller developers who would jump at the chance to build these very cost-efficient projects. This would also avoid a problematic constraint on new housing production: the limited number of builders that can take on larger more complex projects."
London YIMBY proposal for local upzoning 
- Myers, John. "Forget nimbys. Yimby housing policy can transform the UK – with the political will." The Guardian, 11 August 2017.
- Myers, John. “Yes In My Back Yard - How to end the housing crisis, boost the economy and win more votes.’’ Adam Smith Institute, 11 August 2017. https://static1.squarespace.com/static/56eddde762cd9413e151ac92/t/598c8b62be42d6f7f8e30ebe/1502382968482/John+Myers+-+YIMBY+-+Final.pdf.
- Ricco, John. “Houston took this winning approach to adding housing. Could DC do the same?” Greater Greater Washington. September 8, 2016. https://ggwash.org/view/42799/houston-took-this-winning-approach-to-adding-housing-could-dc-do-the-same
- CodeNEXT's transect zones may get eliminated in planned organizational overhaul, officials say 30 June 2017
- How would widespread upzones change Seattle neighborhoods? City releases first findings 8 June 2017
- City’s staff to overhaul CodeNext zones as draft moves to next phase 7 July 2017
- The Bronx Develops: A Metro-North Station in a City Within a City - Norwood News - 14 September 2017
- Homeowners Stand to Gain in Areas to be Rezoned, If They Can Keep Their Homes - Gotham Gazette - 29 April 2017
- The New-New York: Upzoning Neighborhoods in the Era of Bloomberg.
- YIMBY Action (2017). "Call for working group on upzoning San Francisco single-family housing areas." May 2017.