The rising demand for safe human-robot interaction in daily tasks has motivated significant research effort in the robotics field towards compliant and conformable robots, capable of replicating complex human movements in applications such as wearable rehabilitative devices and haptic interfaces. Novel manufacturing, actuation, and sensing technologies contributed significantly to this field by providing design and manufacturing frameworks for inherently compliant robots. Although promising, these technologies are still in the early stages of development and base research for refining their design, improving their performance, and defining design criteria is still required for these technologies to reach their full potential. In this thesis, some of the main challenges hindering the effective application of robotics in wearable devices are tackled. We propose the robotic origami (robogami) framework with multiple but finite degrees of freedom (DoFs) for soft wearable devices. Robogamis are low profile robots that provide conformity and compliance with their multiple DoFs driven by soft actuation methods. The finite DoFs in these robots enable better prediction and planning of their motion while highly customizable joint designs, thanks to the layer-by-layer manufacturing and the precise quasi-2D fabrication processes, allows the multiple DoFs to be embedded to achieve the required level of conformity. The main contributions of this thesis are: -Study of the robogami framework as a design platform for soft robots with programmable reconfiguration and compliance. -Design and validation of actuation solutions based on smart materials for independent actuation of robogami joints. -Adoption of the smart materials' variable mechanical properties to adjust the stiffness of robogami joints and the overall compliance of the robot. -Development of customized sensing methods to measure robogami joint angles and stretchable sensors based on the same principles to measure body movements. We believe that these contributions facilitate some of the main challenges for the effective application of robogamis in wearable devices for safe and yet capable interaction with humans. The highly customizable components can also be used in design frameworks other than robogamis and other applications where compliance and conformity are required.