The quality of life of patients with refractory epilepsy can be significantly improved by designing algorithms capable of forecasting seizures and implementing them into closed-loop advisory/intervention devices. Over the last decade, several algorithms based on neural networks and deep learning have been proposed and showed promising performances. Nevertheless, the computational requirements of such algorithms were major obstacles towards their use in clinical devices. In this work, we overview recently proposed neural network-based seizure forecasting algorithms and summarize the state of the art regarding advancement in hardware design and implementation of deep neural network inferences. The paper ends with a list of recommendation for future seizure forecasting endeavors.