We study the phase diagram of a one-dimensional, two-component (i.e., pseudo-“spin”-1/2) ultracold atomic Fermi gas. The two atom species can have different hopping or mass. A very rich phase diagram for equal densities of the species is found, containing Mott insulators and superfluids. We also discuss coupling such 1D systems and the experimental signatures of the phases. In particular, we compute the spin-structure factor at small momentum, which should reveal a spin gap.