Objective. This paper proposes machine learning models for mapping surface electromyography (sEMG) signals to regression of joint angle, joint velocity, joint acceleration, joint torque, and activation torque. Approach. The regression models, collectively known as MuscleNET, take one of four forms: ANN (Forward Artificial Neural Network), RNN (Recurrent Neural Network), CNN (Convolutional Neural Network), and RCNN (Recurrent Convolutional Neural Network). Inspired by conventional biomechanical muscle models, delayed kinematic signals were used along with sEMG signals as the machine learning model's input; specifically, the CNN and RCNN were modeled with novel configurations for these input conditions. The models' inputs contain either raw or filtered sEMG signals, which allowed evaluation of the filtering capabilities of the models. The models were trained using human experimental data and evaluated with different individual data. Main results. Results were compared in terms of regression error (using the root-mean-square) and model computation delay. The results indicate that the RNN (with filtered sEMG signals) and RCNN (with raw sEMG signals) models, both with delayed kinematic data, can extract underlying motor control information (such as joint activation torque or joint angle) from sEMG signals in pick-and-place tasks. The CNNs and RCNNs were able to filter raw sEMG signals. Significance. All forms of MuscleNET were found to map sEMG signals within 2 ms, fast enough for real-time applications such as the control of exoskeletons or active prostheses. The RNN model with filtered sEMG and delayed kinematic signals is particularly appropriate for applications in musculoskeletal simulation and biomechatronic device control.