Studies on plant electrophysiology are mostly focused on specific traits of action potentials (APs) and/or variation potentials (VPs), often in single cells. Inspired by the complexity of the signaling network in plants and by analogies with some traits of neurons in human brains, we have sought for evidences of high complexity in the electrical dynamics of plant signaling, beyond APs and VPs responses. Thus, from EEG-like data analyses of soybean plants, we showed consistent evidences of chaotic dynamics in the electrical time series. Furthermore, we have found that the dynamic complexity of electrical signals is affected by the plant physiological conditions, decreasing when plant was stressed. Surprisingly, but not unlikely, we have observed that, after stimuli, electrical spikes arise following a power law distribution, which is indicative of self-organized criticality (SOC). Since, as far as we know, these were the first evidences of chaos and SOC in plant electrophysiology, we have asked follow-up questions and we have proposed new hypotheses, seeking for improving our understanding about these findings.