Located in the western part of the county, it borders the following townships: Much of the city of Zanesville, the county seat of Muskingum County, occupies eastern Falls Township, and the census-designated place of North Zanesville is located northeast of the city of Zanesville.

[4] Statewide, the only other Falls Township is located in Hocking County.

By the 1830s, Falls Township had a church, a blast furnace, as well as several mills and factories.

[5] The township is governed by a three-member board of trustees, who are elected in November of odd-numbered years to a four-year term beginning on the following January 1.

There is also an elected township fiscal officer,[6] who serves a four-year term beginning on April 1 of the year after the election, which is held in November of the year before the presidential election.