Praskovya long persuaded her husband to create a shelter where the homeless and needy could receive free treatment and shelter. The couple chose a location for construction on the outskirts of Moscow, beyond the Zemlyanoy Val near Sukharevskaya Square. The initial project was developed by Bazhenov's student, the serf architect Elizvoy Nazarov. The house church in the center of the building divided it into two wings: a hospital and a poorhouse. The convenient entrance for patients was adorned with paired columns.

After his wife's death, Count Sheremetev entrusted his friend, architect Giacomo Quarenghi, with reconstructing the building to make it a majestic monument to his spouse. Nazarov's simple building was to be transformed into a magnificent palace, unparalleled in world architecture.

Quarenghi did not come to Moscow but sent projects and drawings by mail. His ideas were realized by Russian architects Mironov, Dikushin, and Argunov, who built estates for the Sheremetevs in Kuskovo and Ostankino.

Quarenghi replaced the simple portico with a grand semicircular colonnade, giving the building a solemnity. The ends of the wings were decorated with six-column porticos, and four wings were added to the ensemble. The finishing and interior were made from the finest materials; the count spent three million rubles on construction, which was a huge sum.

Nikolai Sheremetev did not live to see the opening of the house, which took place on June 28, 1810, on his birthday, with a large crowd in attendance. The Sheremetev family continued to support the house, donating significant sums for its maintenance.

According to Praskovya Sheremeteva's will, funds were allocated annually for the dowries of needy girls. They drew lots on February 23, the day of Praskovya's memory, and brides-orphans were married in the Trinity Church of the house.

More than 200,000 people received help in this house. Since the beginning of the 19th century, the Moscow branch of the Medical-Surgical Academy was located here. By the end of the century, the hospital strengthened ties with Moscow University and became its clinical base. Leading scientists implemented advanced treatment methods here.

A significant milestone in the history of the house was the work of chief doctor Alexei Tarasenkov. He improved hospital practices, updated medication prescriptions, established control over their purchase and appointment, and organized regular rounds. He proposed opening a free outpatient clinic and a medical fund to assist the sick, which was done.

The Sheremetev hospital repeatedly turned into a hospital. After the Battle of Borodino, wounded soldiers were brought here. On the day the French entered Moscow, the house was emptied, leaving only the infirm and wounded officers. The French, upon learning that this was a charitable institution, posted a guard. However, many valuables were stolen, and a fire damaged the wings. Restoration took several years.

During the cholera epidemic of 1830, no one in the house fell ill.

During the Crimean War, a sanitary detachment was assembled here. In the Russo-Japanese War, a hospital operated. Later, participants of the revolutions were treated here. In 1919, the Moscow City Emergency Station was organized here, and from 1923, one of the buildings of the Sklifosovsky Research Institute of Emergency Medicine was located here. The initiative to restore the house's former glory belonged to surgeon Sergey Yudin.

The chief surgeon of the Sklifosovsky Research Institute, S.S. Yudin, was the elder of the Trinity Church and donated his Stalin Prize for the restoration of its frescoes.

In 1986, the Central Museum of Medicine opened here, which became the Scientific Research Center 'Medical Museum' of RAMN in 1991.

The ensemble of the house, including the main building, wings, gates, and fence, the fresco by Giovanni Scotti, and the bas-reliefs by sculptors Zamarayev and Timofeev, is included in the list of cultural heritage sites and has been added to the preliminary UNESCO World Heritage List.