Group 1: Alkali metals. They react vigorously with water and any other oxidizing agent (esp. halogens) whenever possible, producing explosive heat. The reactivity increases as atomic number increases down the group. They are used in chlor-alkali industrial applications (as what they're named) and act as major reagents in human body (in compound forms)-- NaCl, KCl.

Group 7: Halogens. In contrast, they react vigorously with metals, especially alkali metals, producing also explosive heat. The reactivity decreases as atomic number increases down the group. Chlorine: used in chlor-alkali industry. Iodine, Chlorine and Fluorine are also major reagents in human body. (HCl, NaCl etc.)

Group 8: Noble Gases: They are very very inactive. They basically have no chemical properties as they are so inactive that they wouldn't change to other stuff. However, making of unstable Krypton fluoride, Xenon fluoride and Radon fluoride had been made possible. Noble gases are used as 'anti-reagents' which stops chemical reactiions from taking place. Helium is also used to fill airships for it's lighter than air (1/3~1/4 the weight), Neon is used in light tubes as it glows brilliantly under electric shock, Argon is the major 'anti-reagent' as it is just as heavy as air and the heaviest element that had never been successfully made into reaction (without breaking the nucleus). Krypton and Xenon are heavy gases used as mild 'anti-reagents' when heavy stuff is needed. (Usually Krypton when you need higher stability, while Xenon gives higher density). Radon is a decay chain midst product. No specific uses known.

A footnote: I'm using Mendeleev's groups 1, 7, 8. The IUPAC groups 7, 8 are simply other unrelated things!