Concrete block system, method and connector

A mortarless concrete block system for constructing a structure, the system comprising:

• a plurality of structural blocks made of concrete, each structural block having:
• a top face and a bottom face, the top face and bottom face being substantially L-shaped,
• four lateral faces and a concave inner face extending between top and bottom faces,
• two of said lateral faces being wide lateral faces forming a corner in said block, and
• two of said lateral faces being short lateral faces,
• the concave inner face being located between the short lateral faces and forming a cavity or recess in the structural block;
• at least two of said lateral faces being provided with connecting elements formed and shaped therein;
• a plurality of veneer units, each unit having an exposed face and a rear face, two short lateral faces and two long lateral sides;
• the rear face being provided with connecting elements;
• and
• a plurality of connectors, each being sized, shaped and configured to attach the veneer units to the structural blocks or to attach two structural blocks together, via the respective block and veneer connecting elements, wherein any given connector from said plurality of connectors is suitable for connecting two structural blocks together, or for connecting a veneer unit to a structural block.