This work focuses on continuous future prediction of human upper limb joint kinematics from muscle excitations measured with surface electromyography (sEMG) using a novel neural network training approach. The approach aims at leveraging the inherent lead in EMG signals over observed limb motions to predict joint kinematics forward in time over a short horizon. The correlation-causation relationship between EMG and motion is studied to decode and improve the relationship map between the variables. Unlike a forecasting problem, the presented approach predicts future joint kinematics at each time-step over the established horizon. The prediction horizon was quantified using temporal alignment techniques between normalized EMG excitation signals and motion data. Two studies involving 7 and 10 participants were performed targeting single and multiple degrees of freedom predictions respectively. The proposed training strategy was compared to the general neural network training approach used in other studies that maps current time EMG inputs to current time kinematic label data using 2 popular neural network architectures: back-propagation neural network (BPNN) and time-delayed neural network (TDNN). Models trained using the presented approach consistently showed better training results. The prediction results also showed an improvement of about 5-10 deg in testing RMSE over the model trained without the phase lead with identical input signals for all subjects over multiple motion types and multiple degrees of freedom. Accuracy and generalization performance improvements were further explored by using state information and hybrid architectures. The state-informed hybrid TDNN architecture (SIEMG) substantially improved shoulder and elbow kinematics prediction accuracy to upto 5 deg with respect to the baseline measurements. A hybrid model that combines neuromusculoskeletal modeling and neural network architectures was also developed for single DOF elbow motion prediction that improved inter-subject robustness performance. Data curation methods were further explored to improve intra-subject robustness performance. Also presented is a forward kinematics model using Denavit-Hartenberg (DH) parameterization of the human arm to convert the predicted joint kinematics to wrist joint center pose as task space input for robot teleoperation. Using the proposed SIEMG TDNN models trained with the presented training strategy, the wrist joint center position was predicted with an accuracy of 2-3 cm upto 250 ms forward in time. A real-time prediction framework using pre-trained offline networks was developed in ROS (Robot Operating System) to translate the offline work to online. Simulation results confirm that the offline accuracy can translate well to real-time implementations. The developed architectures and the proposed training strategy could facilitate reduced latency control using EMG.