We disclose methods for 1) the design of neural interfaces, including brain-computer interfaces (BCI), brain-machine interface (BMI), and human-machine interface (HMI) systems that infer motor intent from neural signals acquired non-invasively in healthy persons or in users belonging to clinical populations such as spinal cord injury, stroke, amputees, Parkinson's disease and other physical or neurological disabilities (collectively called 'users'); and 2) how to use those signals by the user to control in close-loop ('user-in-the-loop') wearable exoskeletons, prosthetic or communicative devices to augment, assist or restore the user's cognitive-movement capabilities. The invention also discloses a method for training the users to control BMl-augmented augmentative, assistive or restorative devices.