Maxim the Blessed is known as the first Moscow fool for Christ. According to legend, he left home early and settled on Varvarka near the Church of Boris and Gleb, where he led an ascetic life. In summer and winter, he walked almost naked, enduring heat and cold with prayer, teaching people patience and resilience in the face of life's difficulties. He passed away there, presumably at the church fence, on November 11, 1434. He was buried by Fyodor Kokchin, a neighbor and parishioner of the church. Over time, his surname began to be pronounced as Kochkin, and the church was named "what is at Kochkin's yard." The relics of Maxim were discovered in August 1547, after which he was canonized by the Moscow Church Council as Blessed. An altar dedicated to Saint Maxim the Confessor was added to the wooden Church of Boris and Gleb. No information about the old church has survived. A new church was built in 1698 with funds from merchants Maxim Sharovnikov from Kostroma and Maxim Verkhovitnikov from Moscow.

The church has a cubic shape with a vaulted ceiling and stands on a high basement, representing a one-column chamber. Judging by the laid zakomars and the four-pitched roof, the building had several tiers of kokoshniks, characteristic of architecture from the second half of the 17th century. In the 17th and 18th centuries, the basement was used for storing citizens' belongings during fires.

After the fire of 1737, the church was renovated in the Baroque style, popular in Moscow at that time. This is evident in an old photograph from the early 20th century, where the faceted drum and octagonal vault, characteristic of Baroque, are noticeable. The drum has light windows and is topped with an onion dome. The windows of the upper tier are larger compared to the lower ones. Fragments of 18th-century frescoes have survived in the church and refectory, but the frescoes in the zakomars did not survive. The almost square apse has an unusual shape. The restored design of the stone window frames resembles the rich frames of the 17th century. In 1812, during the invasion of Napoleon's troops, the building suffered minor damage, and services in the church did not cease, although serving in heavily damaged churches was prohibited.

In 1829, a two-tiered bell tower in the Empire style was built, with a high spire, attic, and semi-circular arches. The bells on it are absent.

Among the parishioners of the church were the famous "vodka kings" Smirnovs. Ivan Alexeyevich Smirnov owned a house at the corner of Grusinsky and Ipatievsky lanes, and his vodka was called "Varvarka."

In the 1930s, the church was closed. According to Stalin's plan for the reconstruction of Moscow, all buildings on the southern side of the street were to be demolished, including the Church of Maxim the Blessed. However, the project was not implemented, and the church was preserved. It now adorns the territory of the "Zaryadye" park, created on the site of the demolished "Russia" hotel.

In 1965, under the guidance of architect S.S. Pod'yapolsky, restoration was carried out, and the church premises began to be used for exhibitions. Before the restoration, the church was in a deplorable state: the domes with crosses were missing, decor was lost, the facade paint was peeling, and there were significant damages inside. Since 1994, services have resumed, and the church began to "revive" thanks to the efforts of parishioners, but this was not enough for complete restoration.

During the 2014 restoration, the white stone base was restored, the walls of the church and altars were reinforced. The facades, interiors, frescoes, iconostasis, and fence were updated. The church was painted white, and the bell tower in light ochre with white details. The bell tower's beams were restored, and the metal domes and cupola were restored and painted, with gilding restored on the crosses and spires.

The church's porch was restored with new cladding, recreated in the dimensions of the 19th century with reconstructed fences. The area around the church has been improved, with lawns planted in the earthen areas.