This dissertation considers problems concerning (1) mixing and chemical reaction and (2) heat transfer, in a decaying, homogeneous turbulent flow. Direct numerical simulations have been used to compute the flows numerically in order to measure quantities that are difficult to measure in the laboratory and to test some statistical theories of turbulence by examination of the dynamical variables and their Statistics and Probability; These simulations involve solution of the unsteady Navier-Stokes and mass conservation equations by a pseudo-spectral method in 64[superscript]3, 80[superscript]3 and 128[superscript]3 wave-number domains. Part I deals with the problem of chemical selectivity in turbulent reacting flows with multiple chemical reactions. Part II addresses the problem of scalar transport in homogeneous turbulence with a uniform mean scalar gradient;In Part I numerical simulations were used to study chemical selectivity in the parallel-consecutive reaction scheme(UNFORMATTED TABLE OR EQUATION FOLLOWS)\eqalign A&+ B \buildrel\it k[subscript]1[over]\longrightarrow R R&+ B \buildrel\it k[subscript]2[over]\longrightarrow S (TABLE/EQUATION ENDS)in turbulent flow,where A, B, R and S represent chemical species with R the desired product. The effect of turbulence Reynolds number and other physical parameters on selectivity was determined. The presence of turbulence was found to favor the formation of R over S. It was found that any mechanism promoting homogenization of reactants favors the formation of R, whereas any mechanism sustaining segregation favors the formation of S. Simple first order closure theories for the covariances of the concentration fluctuations were tested and compared with results of the simulations. None of them, however, was found to perform satisfactorily;Part II deals with heat transfer in a homogenous turbulent flow. The evolution of a passive scalar and its transport by a uniform mean scalar gradient was studied using direct numerical simulations and compared with predictions of a two-point statistical theory (direct interaction approximation of Kraichnan, 1964) and with the laboratory experiments of Sirivat and Warhaft (1983). The experiments that were simulated correspond to the "mandoline" (heated wires to introduce the temperature fluctuations) and "toaster" (uniform temperature gradient existing upstream of the turbulence-generating grid) cases. Although the evolution of the scalar field was affected by initial conditions, the asymptotic state appears to be relatively insensitive to the initial conditions. In the absence of a scalar gradient, however, the asymptotic state of the system depends on the initial conditions.