Hydraulic cement compositions that include a carbonate compound composition, e.g., a salt-water derived carbonate compound composition containing crystalline and/or amorphous carbonate compounds, are provided. Also provided are methods of making and using the hydraulic cements, as well as settable compositions, such as concretes and mortars, prepared therefrom. The cements and compositions produced therefrom find use in a variety of applications, including use in a variety of building materials and building applications.