The Anzures area consists of two colonias, Anzures and Verónica Anzures. These used to brush right up, on their east sides, with the Colonia Cuauhtémoc. In fact, the Anzures neighborhoods are from a slightly later period developing in the 1920s, only to give way a decade later to the giant Polanco neighborhood to their west.
Through most of the colonial period, the area was part of the Anzures Ranch. This bordered the Forest of Chapultepec along with several others. Some legends hold that the ranch was originally granted to La Malinche, the infamous interpreter and lover of Hernán Cortés, in the wake of the fall of ancient Tenochtitlan. Such a grant would have coincided with Cortés' division of many other territories along the México-Tacuba Causeway to the north.
The Anzures Ranch was long home to a chapel dedicated to Saint Veronica. This explains the names, then, of both neighborhoods. In the aftermath of the Mexican Revolution, the Central Mining & Investment Company of London renamed the area for old Anzures Ranch. They'd actually purchased it in 1912 but had to wait out the darkest periods of the war. Eventually, they opened a sanitorium named for Weetman Pearson, 1st Viscount of Cowdray, in 1923. This name is still reflected in the ABC (Amercan British Cowdray) Medical Centers around the City, but the original sanitarium stood on the site of the famous Camino Real hotel of today. It's probably the most important landmark in the neighborhood.
Over the years, Anzures developed northward into "Nuevo Anzures." In the late 1920s, that area was renamed Verónica Anzures for the old ranch chapel, then still remembered in the area.
Today both neighborhoods are replete with Californian colonial and some original art deco style homes. Although both styles are less prominent than in Polanco, they still make for wonderful walking streets. The area's most famous resident is easily the Torre Pemex, but both neighborhoods are strong residential communities. As such, they're a bit more private than the mixed-use areas both east and west. Even still, they've also served as important incubating arts neighborhoods for those priced out of Polanco to the west. They share much of the same character as that older, more consolidated gallery scene.