As the global population continues to grow, the demand for housing and infrastructure increases. To tackle the housing shortage, there is a crucial requirement to construct houses rapidly and efficiently. However, the construction industry faces safety concerns and a shortage of skilled workers. Moreover, construction activities contribute significantly to greenhouse gas emissions and generate vast amounts of demolition waste, particularly concrete, which necessitates measures to mitigate environmental impact. To address these issues, substantial innovation is required in the construction industry. Robotic dry-stacking with in-situ (found) materials simultaneously addresses safety concerns and worker shortage while mitigating its environmental impact and improving sustainability, opening up new possibilities in disaster response and remote site preparation. Even though dry-stacking is one of the earliest building techniques used by humans, replicating dry-stacking using robots poses significant challenges, including the lack of available assembly planners and the complexities associated with perception and manipulation. Toward these ends, this dissertation aims to enable robots the capability to dry-stacking freestanding structures with natural stones. The main challenge in robotic construction stems from the irregular shape of the building materials, which involves dealing with complex physical interaction, understanding stability and overall quality, and effective manipulation techniques. This dissertation addresses each of these aspects and systematically investigates robotic dry-stacking planning in both 2D and 3D scenarios. We propose dry-stacking planning based on heuristics and reinforcement learning. To validate the performance of the proposed methods, physical experiments are conducted in both laboratory settings as well as large-scale field environments. Furthermore, a shake table is employed to statistically assess the stability of physical structures constructed by a robotic arm, establishing a connection between stability in simulation and real-world scenarios. We also study the effects of errors in the context of both dry-stacking with irregular stones and collective robotic construction with pre-fabricated bricks. The research presented in this dissertation represents a significant step towards the development of fully autonomous construction systems capable of dry-stacking in-situ materials.