Carbon
This is not technically an alloying element since it is present in all carbon steels. This is one of the most important elements because it usually has the biggest impact on hardenability.
Chromium
Chromium is very hard, when added to steel it helps to improve hardenability, corrosion resistance, and wear resistance.
Molybdenum
This element helps to improve hardenability, tensile strength, and corrosion resistance.
Nickel
This is a major element in steels that need extreme corrosion resistance. Steels with a lot of nickel are usually made into knives for diving in salt water.
Vanadium
This element improves toughness, hardenability, and promotes fine grain growth. The grain growth is very important in how the steel will perform. The manufacturers of the steel do many different tests on the steel to find the best balance of all properties.