The relatively random spiking times of individual neurons are a source of noise in the brain. We show that in a finite-sized cortical attractor network, this can be an advantage, for it leads to probabilistic behavior that is advantageous in decision-making, by preventing deadlock, and is important in signal detectability. We show how computations can be performed through stochastic dynamical effects, including the role of noise in enabling probabilistic jumping across barriers in the energy landscape describing the flow of the dynamics in attractor networks. The results obtained in neurophysiological studies of decision-making and signal detectability are modelled by the stochastical neurodynamics of integrate-and-fire networks of neurons with probabilistic neuronal spiking. We describe how these stochastic neurodynamical effects can be analyzed, and their importance in many aspects of brain function, including decision-making, memory recall, short-term memory, and attention.