Gentle yoga routines for beginners that are easy on the knees and back include poses like Cat-Cow, Child's Pose, and Seated Forward Bend. Cat-Cow stretches the spine and improves flexibility, while Child's Pose gently stretches the lower back and hips. Seated Forward Bend enhances hamstring flexibility without straining the knees. Additionally, poses like Bridge and Reclining Bound Angle Pose help strengthen core and back muscles while reducing pressure on the knees. Always focus on maintaining proper alignment and using props for support if needed.