We outline the recent results on the ground state for a class of one- andtwo-dimensional frustrated quantum spin models with competing ferro(F)- andantiferromagnetic (AF) interactions. Frustrated spin systems are known to havemany interesting properties due to large quantum fluctuations. As a result ofthese fluctuations usual mean-field approach gives quite crude (if not false)description of these systems. Therefore, exactly solvable models are veryinstructive at investigations of such systems. The exact ground state wavefunction of proposed models has a structure of the valence-bond state (VBS)type. One of the 1D model describes the transition line between the F and AFphase. The exact singlet ground state on this line has a double-spiralordering. Using different approximation methods we study the magnetizationcurve in the AF phase. The second considered set of the 1D and 2D models has anexact non-degenerate ground state with exponentially decaying spincorrelations. We also proposed the 1D and 2D electronic models with exactground state represented in terms of singlet bond functions which are thegeneralization of the RVB functions including ionic states.
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