  We present a systematic investigation of attractive binary mixtures in
presence of both spin- and mass-imbalance in one dimensional setups described
by the Hubbard model. After discussing typical cold atomic experimental
realizations and the relation between microscopic and effective parameters, we
study several many-body features of trapped Fermi-Fermi and Bose-Bose mixtures
such as density profiles, momentum distributions and correlation functions by
means of numerical density-matrix-renormalization-group and Quantum Monte Carlo
simulations. In particular, we focus on the stability of
Fulde-Ferrell-Larkin-Ovchinnikov, dimer and trimer fluids in inhomogeneous
situations, as typically realized in cold gas experiments due to the harmonic
confinement. We finally consider possible experimental signatures of these
phases both in the presence of a finite polarization and of a finite
temperature.
