Understanding how biological matter takes its shape is instrumental to biology, bioengineering, medicine, and bioinspired engineering. Gaining information on the principles of morphogenesis could enable clinicians to correct developmental abnormalities, evolutionary biologists to identify evolutionary patterns, developmental biologists to study biophysical principles of morphogenesis, bioengineers to advance tissue engineering, and engineers to develop novel materials and devices. Both physical and chemical events play significant roles in the execution of genetic programs encoded in the chromosomes. Historically, hand-made tools such as tungsten wires, hairs, and glass capillaries have been used in embryology laboratories. Skilled researchers can perform microsurgical interventions with these tools after several years of practice. Nevertheless, the techniques are not easily transferable and are thus reserved for selected researchers. The accuracy, throughput, and speed are quite limited. In order to move from anecdotal evidence to a systematic exploration of biophysical phenomena that take place during morphogenesis, there is a need for a versatile motorized platform that can gently yet precisely and rapidly manipulate embryos while assessing the physical properties of the manipulated tissues. This thesis presents an integrated approach to advance the understanding of the mechanics of morphogenesis and development in vertebrates, primarily through modernizing the classical experimental embryology techniques via robotics and automation. A user-friendly robot-assisted microsurgery platform that enhances precision, reproducibility, and accessibility in manipulating soft tissues is introduced. Using this platform, specific regions in the tail of the embryos of zebrafish - a widely used model in vertebrate development - are surgically manipulated. Advanced microscopy techniques are used to quantify changes in the shape and structure of the explants and the internal segmentation clock dynamics. Findings revealed a critical interplay between the posterior notochord, tailbud, and presomitic mesoderm, as well as the robustness of somite patterning against structural perturbations. As a further upgrade to the robotic platform, automated microsurgery is realized, which brings further precision, accuracy, and speed compared to teleoperation. A non-invasive technique to measure tissue mechanics is introduced based on optical elastography. A fully customizable experimental platform accompanied by an image processing toolbox is developed to measure the elasticity of viscoelastic substrates. The elasticity of hydrogels of varying concentrations is reported by imaging the propagation of shear waves in the transparent sample at high speed. The robotic systems described in this thesis interface high-precision and dexterous microsurgical manipulation with life science research, particularly in embryology. The reported techniques and results set the stage for a better understanding of the mechanics of tissue morphogenesis during vertebrate development.