Methods of capturing or sequestering carbon include introducing a reaction gas stream to a catalytic converter to convert a portion of the carbon in the carbon oxide to solid carbon and a tail gas stream containing water vapor, removing the solid carbon from the catalytic converter for use, disposal, or storage, and recycling at least a portion of the tail gas stream to the catalytic converter. Methods may also include removing a portion of the water from the tail gas stream. The tail gas stream includes a portion of the initial process gas stream and at least a portion of water vapor produced in the catalytic converter. Methods may also include removing water vapor from various streams and reacting the carbon oxide with a reducing agent in the presence of a catalyst. Systems for capturing or sequestering carbon from a gaseous source containing carbon oxides are also described.