Wikipedia says Indianapolis created the world's first union station in 1848. That means one shared station for several railroads instead of one for each. The station building opened on September 20, 1853.
The larger station you see today opened in September 1888. Pittsburgh architect Thomas Rodd designed it in the Richardsonian Romanesque style. It is built of granite and brick, trimmed with Hummelstown brownstone, and it has an enormous rose window and a soaring 185-foot clock tower.
The head house and clock tower of this second station still stand. Amtrak's Cardinal line serves the station today, from a waiting area beneath the train shed.