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 d. 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 p-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.