The invention is for a modular building unit (10, 200, 210) for use in constructing a building. The building unit (10, 200, 210) has a planar body (12) having two major side faces (12.1) and two ends (12.2) between each side face (12.1), and a connection interface (28, 30) provided at each of the ends, for connecting similar building units (10, 200, 210) with complemental connection interfaces. The body (12) comprises three walls (14, 16, 18) arranged side-to-side and transversely spaced from each other, the three walls (14, 16, 18) thus defining two planar spaces (20, 22) therebetween, and a plurality of reinforcing webs (24) in the first space, for providing structural support to the building unit (10, 200, 210). The second space (22) defines at least one hollow cavity for receiving a matched insulation insert (25) thereby to impart insulating properties to the building unit (10, 200, 210).