There is an increased interest in cilsunar missions, i.e., missions in the Earth-Moon space due to their strategic importance. Many of these missions will use Solar Electric Propulsion (SEP) due to its lower propellant usage. However, SEP has significantly lower thrust compared to traditional chemical propulsion resulting in a significantly higher flight time. Moreover, cislunar spacecraft experience the three-body dynamics due to the presence of the Earth and the Moon. The three-body dynamics are extremely non-linear, chaotic, and computationally expensive to solve. This dissertation explores the use of Machine Learning and Artificial Neural Networks (ANN) to aid in cislunar path planning and control while using easier-to-solve low-fidelity spacecraft dynamics. First, an online single-layer neuro-adaptive estimator called Modified State Observer (MSO) is used to capture the unmodeled perturbations acting on a spacecraft operating in the cislunar space. The performance of the developed algorithm is investigated through numerical simulations, demonstrating significant reduction in modeling errors. Then a multi-layer off-line ANN is used to learn and predict the unmodeled dynamics in low-trust multi-revolution cislunar missions. The ANN-based dynamics prediction scheme results in significantly lower errors for subsequent revolutions. Finally, the MSO is combined with a Non-Linear Dynamic Inversion (NDI) controller to create a neuro-adaptive control scheme for cislunar spacecraft. Exploring the effectiveness of the control law, it is seen that while the control scheme works, it cannot realistically provide control for a low-thrust spacecraft with reference trajectory designed in the very low-fidelity CR3BP model. However, it demonstrated good reference-tracking with low thrust, in the case of trajectory designed in high-fidelity dynamics experiencing unmodeled perturbations due to a Missed Thrust Event (MTE).