The largest measurement system still in use today in the west rooted in traditional units is the British (Imperial) And US customary system. The origins of the units can be traced back to Roman, Carolingian and Saxon roots which is the reason many of the unit names are familiar to other European indigenous measuring systems with equally long history.
The British (Imperial) and US customary system are in fact two separate but closely interrelated systems whereas the US customary system is based on the British system as it was defined during the American Revolution in the late 18th century. Once the Unites States was separated from the United Kingdom they did not consider to update their measuring system when the United Kingdom decided to redefine many units in 1824 in what we today call the British (Imperial) system.
An example of the confusion this can bring is that the United States stated in 1893 that a yard equals 3600/3937 = 0.9144018 metres. Three years later the British fixed the yard to be 0.9143993 metres. Not a large difference but with time and the need for greater precisions in measurement this has become an issue of confusion. As a consequence United Kingdom, United States, Australia, Canada and South Africa standardized a third type of yard called the international yard in 1960 with the length equaling 0.9144 metres exactly.
Most English speaking countries have since the 1960s undergone metrication programs where the traditional measurement systems have been exchanged for the metric system. Great Britain has regulated use of the metric system in many areas with some interesting exceptions like road signs and beer sizes. So for the continental European driver it might be a surprise to notice traffic signs written in miles per hour when crossing the channel.
The United States use the metric systems in certain areas but many fields still use the customary system. Car manufactures have used the metric system but the aircraft manufacturers have relied on custom units. A sad example of this was the NASA $125-million dollar Mars Climate Orbiter lost in space in 1999 due to unit mismatches. The navigation team working at Jet Propulsion laboratory in Pasadena had been working in the metric system but the spacecraft engineers of Lockheed Martin in Denver who built the spacecraft calculated acceleration values in feet and pounds. When combined the result was a costly crash.
The units which not were around in the beginning of the 19th century have been introduced in the Imperial system afterwards by using the metric counterparts. So for example the Imperial system uses the volt for measuring potential difference and ampere for measuring electric current though these units are defined in terms of metric base units instead of yards and pounds.