Throughout history, different cultures and civilizations have used a variety of symbols to represent numbers. Some of the most significant systems of numerical notation that have been developed include:

1. Babylonian numerals: This system was used by the ancient Babylonians, and was based on a sexagesimal (base 60) system. The Babylonians used a combination of symbols to represent numbers, including wedges, dots, and curved lines.
2. Egyptian hieroglyphs: The ancient Egyptians developed a hieroglyphic system of writing that included symbols for numbers. They used different symbols for different powers of ten, and also developed a separate system for fractions.
3. Roman numerals: The Romans developed a system of numerals based on letters of the alphabet. They used seven basic symbols to represent numbers, with different combinations of these symbols used to represent larger numbers.
4. Hindu-Arabic numerals: This is the numeral system that is most commonly used today, and was developed in India in the 6th or 7th century CE. The Hindu-Arabic system uses ten digits (0-9) and a place-value system to represent numbers of any size.

In addition to these systems, there have been many other systems of numerical notation developed throughout history, including the Mayan numerals, the Chinese numerals, and the Greek numerals. Each of these systems has its own unique set of symbols and rules for representing numbers, and has played an important role in the development of mathematics and science.