Parallel layers of fermionic atoms offer rich new physics. One species of fermionic atoms (A) is constrained to move only on two thin layers separated by distance . Another species (B) is free to move in three-dimensional space. (a) At large interlayer separation, the A atoms only interact within a layer as they are dominated by -wave interaction, forming a BCS-type pairing as shown by the rotating atoms. (b) If the interlayer spacing is small, the A atoms will pair up across layers. (c) If the interaction between A and B species is strong, they will form “molecules” or (d) three-body Efimov states involving A atoms in each layer and a B atom.