Court of Appeals Hall, originally known as State Hall, was designed by architect Henry Rector to house State offices. The Greek Revival structure was completed in 1842. The capitals and bases of the five columns supporting the portico were copies of those of the ancient Greek Temple of Nike Apteros on the Acropolis. Architectural historian Talbot Hamlin opined in 1944 that the building "proclaimed the complete victory of the Greek Revival in the Albany region".
In 1916, the State offices were removed to other quarters and the building was remodeled to house the Court of Appeals. State Architect Lewis F. Pilcher designed a rear addition into which was moved the beautiful Courtroom, until then located on the third floor of the Capitol. Designed by Henry Hobson Richardson in 1881, the Courtroom, with its elaborate hand-carved oak paneling, furniture, and marble and Mexican onyx fireplace, is one of the finest nineteenth century governmental chambers. According to the Preservation League of New York State, "the dual preservation of a noble Greek Revival building and Richardson's sumptuous courtroom was an early triumph of historic preservation".
The Court completed a thorough renovation and expansion of Court of Appeals Hall in 2003, modernizing utilities, communications and fire safety systems that had become badly outdated since the last major renovation was undertaken in 1958. Two additions at the back corners of the building increased floor space by a third, allowing all seven judges to be housed on the same floor for the first time. The additions to the building are faced with marble from the same Danby, Vermont quarry that supplied the 1958 project. Brass chandeliers based on 1883 designs by H. H. Richardson were reproduced for the courtroom, the high groin-vaulted ceilings of the 1842 structure were re-opened to view in key public areas of the first floor, and the oculus at the top of the dome was restored in a manner consistent with the original building design. A favorite feature from the prior renovation, the 1000 square foot "Romance of the Skies" mural inside the dome, was painted by Eugene F. Savage in 1959.