Wearable robots for the legs have been developed for gait rehabilitation training and as assistive devices. Most devices have been rigid exoskeletons designed to substitute the function of users who are completely paralyzed. While effective for this target group, exoskeletons limit their users' contributions to movements. Soft wearable robots have been suggested as an alternative that allows, and requires, active contributions from users with residual mobility. In this work, we first tested if the MyoSuit, a lightweight, lower-limb soft wearable robot, affected the walking kinematics of unimpaired users. Secondly, we evaluated the assistance delivered to a patient with a gait impairment. In our first study, 10 unimpaired participants walked on a treadmill at speeds between 0.5 and 1.3 m/s. We found that wearing the MyoSuit in its transparency mode did not affect the participants' walking kinematics (RMS difference of joint angles <; 1.6°). Step length and the ratio of stance-to-stride duration were not affected when wearing the MyoSuit. In our case study with one spinal cord injured participant, the MyoSuit supported the participant to increase his 10 MWT walking speed from 0.36 to 0.52 m/s, a substantial clinically meaningful improvement. Our results show that the MyoSuit allows user-driven, kinematically unaltered walking and provides effective assistance. Systems like the MyoSuit are a promising technology to bridge the gap between rigid exoskeletons and unassisted ambulation.