First, I present recent work describing ultra-cold fermions with three internal states and tunable singlet s-wave interactions. I show that the evolution from BCS to BEC superfluidity exhibits just standard crossover physics, where the third state is effectively inert even in the case of SU(3) symmetric interactions. I label these three internal states by colors and show that the introduction of color-orbit and color-flip fields transforms a conventional color superfluid into an unconventional one, which does not reside in the domain of color superconductivity of quantum chromodynamics. The BCS to BEC evolution involves several topological quantum phase transitions between novel color superfluid phases that include gapless superfluids with quintuplet pairing [1, 2, 3]. Second, I discuss ultra-cold fermions with four internal states and tunable singlet s-wave interactions and make a connection to multiband superconductors found in the context of condensed matter physics. I review some early work about the evolution from BCS to BEC superfluidity on multiband systems [4, 5, 6] and present recent unpublished work covering the phase diagram, as well as, spectroscopic and thermodynamic properties of these systems at low temperatures. Such properties are functions of the parameters of the Hamiltonian, namely, interactions, band offset and Josephson coupling and, depending on their values, qualitative changes in the energy spectrum and population imbalances occur .
 D. M. Kurkcuoglu and C. A. R. Sá de Melo, “Color superfluidity of neutral ultracold fermions in the presence of color-flip and color-orbit fields”, Phys. Rev. A. 97, 023632 (2018)
 D. M. Kurkcuoglu and C. A. R. Sá de Melo, “Creating spin-one fermions in the presence of artificial spin–orbit fields: emergent spinor physics and spectroscopic properties”, J. Low Temp. Phys. 191, 174 (2018).
 D. M. Kurkcuoglu and C. A. R. Sá de Melo, “Quantum phases of interacting threecomponent fermions under the influence of spin-orbit coupling and Zeeman fields”, arXiv:1612.02365v1 (2016).
 M. Iskin and C. A. R. Sá de Melo, “BCS-BEC crossover of collective excitations in two-band superfluids”, Phys. Rev. B 72, 024512 (2005).
 M. Iskin and C. A. R. Sá de Melo, “Two-band superfluidity from the BCS to BEC limit”, Phys. Rev. 74, 144517 (2006).
 M. Iskin and C. A. R. Sá de Melo, “Evolution of two-band superfluidity from weak to strong coupling”, J. Low Temp. Phys. 149, 29 (2007).
 Yue-Ran Shi, Wei Zhang and C. A. R. Sá de Melo, “Thermodynamic and spectroscopic properties of two band superfluids with tunable interactions or densities”, in preparation (2020).