The demand and the potential for automation in the construction sector is unmatched, particularly for increasing environmental sustainability, improving worker safety and reducing labor shortages. We have developed an autonomous walking excavator - based one of the most versatile machines found on construction sites - as one way to begin fulfilling this potential. This article describes the process of converting an off-the-shelf construction machine into an autonomous robotic system. First we outline the necessary sensing equipment for full autonomy and the novel actuation of the legs, and compare three different complementary actuation principles for the excavator's arm. Second, we solve the state estimation problem for a general wheeled-legged robot. Beside kinematic measurements, it includes GNSS-RTK, to absolutely reference the machine on a construction site. Third, we developed individual controllers for driving, chassis balancing and arm motions allowing for fully autonomous operation. Lastly, we highlight the machine's potential in four different real-world applications, e.g. autonomous trench digging, autonomous assembly of dry stone walls, autonomous forestry work and semi-autonomous teleoperation. On top, we also share some development insights and possible future research directions.