Frobel's idea was developed by Gustav and Otto Lilienthal, two brothers who were both Architects. They created artificial stone blocks using quartz sand, chalk and linseed oil and colored by dyes which looked like miniature bricks, sandstone and slate. Their building toys were much more stable than the ones produced for Frobel. Unfortunately they were not good businessmen so failed to sell their products but Friedrich Adolf Richter took their idea and started the Anchor Stone company in Rudolstadt, Thuringia Germany and these blocks became world famous.
Another great influence in the toy building kit we see today were the alphabet bricks which were used to teach young children particularly in preschool nurseries.
The next development in building toys were the interlocking tongue-and-groove joints introduced by Charles M. Crandall. In 1867 he took over his father's woodworking shop in Covington, Pennsylvania and changed the emphasis to toy making. His interlocking blocks allowed children to create many different figures particularly circus acrobats. This ability to be able to create different "models" with one toy building kit was taken a step further by Frank Hornby in 1901 whose metal strips with holes which could be joined together by nuts and bolts led to the "Mechanics Made Easy" kits or Meccano as we know it now.
The introduction of plastic has of course given manufacturers the ability to create construction sets which adhere to very tight specifications. Lego was introduced by Ole Kirk Christiansen in 1932 firstly with wooden blocks but it was the introduction of the plastic bricks which gave us the construction toys we know so well today.
So the building toys of today were developed from the classic building toys of the past. Today's Lego, Knex and Clics were foreseen in the 1860's and baby building blocks were first thought of by Friedrich Frobel who was born in 1782.