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This dissertation is concerned with gradient-based optimization or ”learning” in spiking neural networks and their applications. Based on a method well known in the optimal control literature, I derive a novel algorithm ”Event- Prop,” which computes exact gradients for arbitrary loss functions and allows for the optimization of spiking point neural networks. In the special case of time-invariant linear systems with jumps, this suggests an exact integration algorithm. Based on the same starting point, it is also possible to derive approximate online learning rules for spiking point neurons. More broadly, the adjoint method with jumps can be applied to structured neurons and other dynamical nets. In the case of structured neurons, the adjoint equations couple so that they can be interpreted as being associated with the same physical struc- ture. This partially resolves the weight transport problem. Finally, I turn to the question of how stochastic classical systems, such as networks of deterministic spiking neurons stimulated by Poissonian noise, can emulate properties of small quantum systems.