Developing deep neural network-based controllers that adapt in real-time with stability guarantees is a challenging task. In my 2022 result, I developed the first DNN-based controller with Lyapunov-based adaptation techniques, solving a 25 year old open problem, enabling it to maintain stability while learning from its environment. From that work has emerged a new class of adaptive control strategies, termed Lyapunov-based neural networks (LbDNNs), that leverage the strengths of deep learning while ensuring robust performance in the face of uncertainties. More recently, I have been exploring the integration of LbDNNs with other machine learning techniques to further enhance their adaptability and performance. The result has been extended to solve various problems such as robot herding, model-based reinforcement learning, multiagent target tracking, adaptive safety, stochastic control, physics-informed learning, output feedback control.