Soft robotics is an emerging field, with its application in diverse fields including surgical, collaborative, space, and agricultural robots. Unlike rigid robots, the continuum nature of soft materials provides soft robots with an infinite degree of freedom. This has led to challenges in modeling, feedback (shape reconstruction), and control. Consequently, researchers have explored a new class of modeling, sensing, and control algorithms for such systems. This dissertation focuses on the shape reconstruction of the soft and continuum manipulators using non-contact sensors and geometric modeling. Reliable and accurate reconstruction of the manipulator shape without interfering with their dynamics is foreseen to have a high impact on the control of soft continuum manipulators. The challenges in robot shape reconstruction arise from their continuum nature, high deformability, non-linear dynamics, and, unknown material properties. Various studies have combined inductive, magnetic, resistive, and optical sensor feedback with physics-based and geometric models to deduce the manipulator shape. However, they are intrusive and economically expensive. Existing machine learning and finite element methods (FEM) based approaches fail in real-time. Consequently, reduced order models are necessary to compute the shape. For shape reconstruction, sensors are required to acquire the physical parameters.In this research, the manipulator shape is reconstructed by incorporating feedback from a camera (vision, providing position) and IMUs (providing slope) with a geometric model of the manipulator backbone. The geometric model is a multi-segment piecewise continuous quintic Pythagorean-Hodograph (PH) curves. Two different base algorithms are constructed: position-based and slope-based methods. Position based method is used with vision while the slope-based method is used with IMU sensor data. The shape reconstruction is formulated as a constrained optimization problem that minimizes the curve bending energy with nonlinear length, position, and slope constraints. The robustness (equivalently, stability) of the algorithm is investigated by inducing noise to the sensor measurements. Lastly, sensor fusion of both methods is developed for scenarios when sensor data is not available for both sensors. The experiments were conducted on a soft, agile tensegrity manipulator for different planar static poses. This work paves a path for shape reconstruction of soft manipulators in real-time using multi-sensor data.