This review deals with theoretical studies on tetratomic molecules in a non-degenerate electronic state. The potential energy surfaces are mapped, using accurate ab initio methods, in the internal coordinates including the three stretching distances (R₁, R₂, R₃), the two in-plane bending angles (θ₁, θ₂) and the out-of-plane angle (τ). Several examples will be treated with an increasing complexity: NCCN (linear molecule), N₂CO⁺ (weakly bound tetratomic system) and c-C₃H^- (formaldehyde type molecule), for which the potential energy surface presents only one minimum along the torsion coordinate τ. The spectroscopy of such molecules is viewed to be more complicated than it is the case for smaller systems. In addition, the assignment of the rovibrational levels is more complicated due to anharmonic resonances. The fourth part of this review treats the spectroscopy of the HONO molecule which presents two stable configurations cis and trans. These two forms are separated by a potential barrier of 4100 cm^-1. The study of the trans-cis isomerisation, due to tunneling effect through this barrier, has revealed the efficiency of this process even for vibrational levels located well below this barrier (efficiency greater than 5%  for  levels  lying  above  2700 cm^-1). The coupling between the torsion and the ON middle stretch is found to play a crucial role during the isomerization process. Finally and in the ONNO⁺ and t-H₂N₂⁺ cases, we will show how the couplings (such as vibronic interactions, Renner-Teller effect and spin-orbit couplings) may complicate the mapping of the potential energy functions and the spectroscopy of such systems.