A magnetic building block playing system has magnetic building blocks for building miniature models of imaginary or historic buildings and settlements. The basic element of the system is a magnetic building block with the following characteristics: (a) it has a cuboid shape of brick size; (b) its base material is an ordinary plastic material (for example ABS) and its magnetic material is a magnetisable thermoplastic material; (c) its magnetic coupling points are shaped as squares or circles with axially symmetrical, overlapping inner and outer surfaces; and (d) it is magnetised so that the inner and outer surfaces of the coupling points are unlike, so that the coupling points of two surfaces to be coupled are oppositely poled.