The lawn edger most people used before they became mechanized was a shovel, spade or a half-moon shaped tool. The half-moon shaped tool often had a lip on top to prevent it from being completely driven into the ground. This tool isn't a relic of history as it is useful in modern times as well. The first patent applied on a lawn edger was in 1914 in Denver, Colorado, and it was a handheld tool with sharp blades facing in opposite directions.
Some of the first patents filed for a mechanized edger show designs that are remarkably similar to modern machines. They involve pulleys, a motor and cutting blade. The blades may be different, blades may be similar to a circular saw vs. a lawn mower blade, or the configurations may be different, but the basic concepts were the same. Soon models were designed that had adjustable cutting blades that would cut both horizontally and vertically. Combinations began to emerge that seemed similar to the modern weed whacker but with a blade rather than a string.
The 1960s saw general variations on the same pulley-motor-blade mechanism. Designs were emerging that combined lawn mower and edger functions using convertible blade mechanisms. In the 1970s some specialty lawn edgers were invented, such as the sand trap trimmer and right- or left-handed trimmers. Later, trimmer line was introduced as a replacement for the blades. The trimmer line was supposed to be less damaging to structures, like buildings or fences.
Line trimmers were touted as being very useful as lawn edgers. A simple change in the angle would change the cut from horizontal to vertical. Now that lawn edgers were more popular, parts and add-ons started to emerge. A carriage was invented that offered more stability and evenness to this type of edging, but apparently didn't do well on the market because they don't exist as an option today. Blades started to be applied to string trimmers.
The 2000s saw constant improvements, combinations and reconfigurations. There was an aerodynamic cutting line invented that blew the grass away as it was trimmed. Some models offered two handles, like a rototiller, for stability and more controlled steering. Also, the profiles were narrower on some. Multipurpose tools appeared that could mow, trim, edge and blow the grass away. Despite this, most landscapers and homeowners use machines that aren't so different from the first motorized edgers or will simply use a line trimmer at an angle to do their lawn edging.