This paper introduces two novel event-driven learning algorithms for spiking neural networks (SNNs): Spike-Timing-Dependent Event-Driven (STD-ED) and Membrane-Potential-Dependent Event-Driven (MPD-ED). These algorithms leverage precise neuronal spike timing and membrane potential, respectively, to enable effective learning in SNNs. The proposed methods are evaluated on static and neuromorphic datasets, demonstrating superior performance compared to existing event-driven counterparts. On the CIFAR-100 dataset, STD-ED achieves 94.33% accuracy, while MPD-ED achieves 94.84% accuracy. The methods also show significant energy efficiency, with on-chip learning experiments achieving a 30-fold reduction in energy consumption compared to time-step-based surrogate gradient methods. The STD-ED algorithm uses an Adaptive Firing Threshold-based Integrate-and-Fire (AFT-IF) neuron to address over-sparsity and gradient reversal issues. The MPD-ED algorithm integrates the AFT mechanism into spiking neurons and uses a masked surrogate gradient function to implement the MPD-ED approach. Both methods are shown to effectively address the challenges of event-driven learning in SNNs, offering promising avenues for energy-efficient applications in neuromorphic computing.This paper introduces two novel event-driven learning algorithms for spiking neural networks (SNNs): Spike-Timing-Dependent Event-Driven (STD-ED) and Membrane-Potential-Dependent Event-Driven (MPD-ED). These algorithms leverage precise neuronal spike timing and membrane potential, respectively, to enable effective learning in SNNs. The proposed methods are evaluated on static and neuromorphic datasets, demonstrating superior performance compared to existing event-driven counterparts. On the CIFAR-100 dataset, STD-ED achieves 94.33% accuracy, while MPD-ED achieves 94.84% accuracy. The methods also show significant energy efficiency, with on-chip learning experiments achieving a 30-fold reduction in energy consumption compared to time-step-based surrogate gradient methods. The STD-ED algorithm uses an Adaptive Firing Threshold-based Integrate-and-Fire (AFT-IF) neuron to address over-sparsity and gradient reversal issues. The MPD-ED algorithm integrates the AFT mechanism into spiking neurons and uses a masked surrogate gradient function to implement the MPD-ED approach. Both methods are shown to effectively address the challenges of event-driven learning in SNNs, offering promising avenues for energy-efficient applications in neuromorphic computing.