This article explores models of causality of the physical universe which extend beyond the usual quantum and classical descriptions. To facilitate discussion of this topic, a brief review of relevant areas of modern physics is included. Although mathematical logic is not directed in time, the causal description of the physical universe is classically performed in terms of temporal determinism, an initial-value problem in which subsequent states are determined through the action of differential equations, thus avoiding the paradox of effects preceding their causes. Quantum mechanics has reduced this description to the status of a stochastic-causal theory, in which individual future states of a system are not predictable because the probability interpretation of the wave function prevents a complete knowledge of a single reduction of the wave packet. The transactional interpretation of quantum mechanics provides a basis for examining the workings of stochastic causality in terms of time-symmetri c advanced and retarded waves. Cosmic symmetry-breaking provides a contrasting description in which time-directed phenomena derive their explanation. Dual-time supercausality replaces the stochastic model with one in which two complementary causal processes, symmetric- time and directed-time are operating. The mode of interaction of these avoids temporal paradox in the time- directed description, and also explains why quantum mechanics provides an incomplete stochastic model. An important role for supercausal processes in the structural evolution of the universe is proposed, including the emergence of biosystems, biological evolution, and consciousness. 1 : CAUSALITIES AND SUPERCAUSALITIES Since the development of calculus and the Newtonian model of the universe, the evolution of dynamical events has been described through the directional application of time as a parameter. The evolution of a classical system can in principle be causally described in terms of the initial conditions and the differential equations governing its action. In the classical Laplacian universe, the initial conditions and the dynamical equations taken together completely specify the ongoing state at subsequent times. We will refer to this model as temporal determinism. The classical Hamiltonian and Lagrangian dynamical equations are both expressed as differential equations expressing generalized coordinates in terms of increasing time, where = T - V and in the case of a potential, = T + V, giving the total ( T kinetic & V potential ) energy :