Drawn thread work
Drawn-thread work is generally considered to be among the first types of true lace. It was created by taking ordinary linen, and pulling out certain threads, or cutting other threads, to create spaces in the linen, and stitching around the holes to makes sure they remained strong. This is similar in principle to modern hardanger - but hardanger itself is very much out of period.
The holes were not at first left completely empty. Any remaining threads were left as a framework for embroidery in elaborate patterns. This style was known as Reticella.
Laces made in this fashion were quite popular and were used in collars, cuffs and table-ware. Often mixed with elaborate embroidery, including beautiful pieces where there are alternating squares of embroidered fabric with 'non-squares' of reticella lace.
Patterns were constrained by the warp and weft of the fabric itself. Having to draw out the threads was also difficult, this added to the fact that the lacier it becomes (ie the more threads you draw out), the flimsier the framework is.
Eventually, lace-makers didn't bother drawing threads out and simply cut out a space and built their framework in the gap - which became known as "Punto in Aria" = "points in the air".