Soft robotic systems are inherently safe for human interaction and are able to perform useful tasks such as grasping or locomotion. Reliably producing the complex, monolithic, 3D structures necessary in these systems remains a challenge due to limitations in the available manufacturing methods. Historically, these systems have been made with molding, casting, stamping, and other techniques. Unfortunately, these methods are largely limited to 2D and thus inhibit the robots' potential complexity. Recent advances in 3D printing of elastomers and other low-modulus materials has enabled us to manufacture soft structures that were not obtainable just 5 years ago. Taking advantage of this leap in manufacturing capability, my work explores the improvements to soft actuators, sensors, and integrated robotic systems afforded by 3D printing. In the realm of soft actuators, I first describe the development of an entirely 3D printed continuously variable transmission which increases the output force of tendon-driven actuators by up to 3X without negatively impacting its unloaded speed. Additionally, I describe the development and characterization of a soft limb which uses tendon-routing variations to achieve complex motions and improved stiffness profiles. Further, I describe the development of haptic sensors by directly printing them using Direct Ink Writing, and by printing their structure for integration with off-the-shelf and molded components. Finally, I discuss the integration of these soft sensors and actuators in the development of two 3D-printed soft robotic systems: i) a hand which uses its reflexes to catch a ball and crush a can, ii) a crawling robot which demonstrates improved locomotion due to complex tendon routing schemes, and iii) an optoelectronically innervated soft prosthetic hand which can detect softness and shape.