This chapter presents the basics of the mathematical formalism and methodologyof the prequantum classical statistical field theory (PCSFT). In theBild-conception framework, PCSFT gives an example of acausal theoretical model (CTM) beyond QM, considered as observationalmodel (OM). Generally CTM-OM correspondence is not as straightforwardas in Bell’s model with hidden variables. In PCSFT hidden variables are randomfields fluctuating at spatial and temporal scales which are essentiallyfiner than those approached by the present measurement technology. Thekey element of the PCSFT-QM correspondence is mapping of the complexcovariance operator of a subquantum random field to the density operator.For compound systems, the situation is more complicated. Here PCSFT providestwo descriptions of compound systems with random fields valued intensor vs. Cartesian product of the Hilbert spaces of subsystems. The lattermodel matches representation of compound systems in classical statisticalmechanics. Both approaches are used for measure-theoretic representationof the correlations violating the Bell inequalities.