Using magnetic susceptibility, specific heat, electron-spin resonance (ESR), nuclear magnetic resonance (NMR), neutron diffraction, broad-band dielectric spectroscopy, infrared optic spectroscopy and thermal expansion we investigated spin, orbital, charge and lattice correlations in ternary magnetic chalcogenide spinels AB2X4 with A= Fe, Mn, Hg, Cd, Zn; B=Cr, Sc; X=O, S, Se. An orbital liquid state was found to realize above the orbital ordering temperature of 10 K in FeCr2S4 with Jahn-Teller active A-site Fe2+ cations. It is characterized by a large linear contribution to specific heat of about 100 mJ/mol K2. In electronically doped FeCr2S4 a quadratic term in the temperature dependence of the specific heat below 3K down to 50 mK reveals a novel state of the orbital glass supported by the dielectric properties [1]. Inelastic neutron scattering on strongly geometrically frustrated FeSc2S4 evidences a state of spin-orbital liquid with a clear signature of the dynamic Jahn-Teller effect. The spin excitations in the liquid state show a strong dispersion typical for a supercooled paramagnet with a spin gap of 0.2 meV [2]. The magnetic structure of the spin-frustrated MnSc2S4 was found to be a complex spiral in the a-b plane with a propagation vector (¾, ¾, 0). Although the magnetic correlations show up below 23 K, the long range magnetic order is suppressed down to a temperature TN=2.3 K~ΘCW/10. The magnetic ordering is characterized by an incommensurate modulation at TN and a locked-in commensurate structure below 1.9 K [3]. Nuclear magnetic resonance studies on 45Sc ions in frustrated MnSc2S4 found a behavior of a long-range ordered antiferromagnet with the onset of spin fluctuations at unusually high temperature of ~40 TN. Orbital fluctuations strongly enhance the spin-lattice relaxation rate in FeSc2S4 at elevated temperatures. Slowing down of the orbital fluctuations at low temperatures results in an increase of the spin-spin relaxation rate [4]. CdCr2S4 was recently discovered to be the first spinel with multiferroic properties in which the ferromagnetic ordering coexists with the relaxor ferroelectricity [5]. On approaching the Curie temperature of 84.5 K the dielectric constant shows a strong increase and a magnetocapacitive coupling reaching a colossal value of 3000 % for a field of 10 T. Even higher magnetocapacitive coupling was found in another multiferroic, HgCr2S4, which exhibits metamagnetic behavior and a complex spiral antiferromagnetic order below 22 K. The dielectric constant becomes strongly enhanced below 60 K, which is ascribed to polar dynamics governed by the appearance of strong ferromagnetic correlations [6]. Infrared spectroscopy studies on ZnCr2S4 spinel reveal a splitting of the low-frequency phonons at the transition temperature from incommensurate spiral antiferromagnetic order to commensurate collinear order at 8 K [7]. Specific heat and thermal expansion exhibit a second anomaly at this temperature beside the anomaly at the onset of the spiral order at 15 K. The anomalies in the specific heat and thermal expansion and phonon splitting at 8 K are strongly suppressed by magnetic fields that suggest the spin-driven origin of the structural transformation at 8 K. The found new effects and ground states are attributed to competition of charge, spin and orbital degrees of freedom, which are strongly coupled to the lattice. The concepts of geometrical frustration related to the tetrahedral arrangement of the magnetic ions on A and B cationic sites of the spinel structure and of bond frustration due to competing ferromagnetic and antiferromagnetic exchange interactions are used in considering the origin of the observed phenomena.