Weeds are plants that frustrate gardening or landscaping goals. Like other plants, weeds are categorized as perennial, annual, grassy, broadleaf, and woody, and are managed accordingly.
Unfortunately, some weeds are so aggressive and difficult to control that they are labeled ‘noxious’.
Executive Order 13112 (February 3, 1999) identifies noxious weeds as “an alien species whose introduction does or is likely to cause economic or environmental harm or harm to human health” and are required to be controlled by law.
Such weeds are identified on a state-by-state basis because their aggressiveness is often a function of the environment. Each state has specific laws governing their control.
Many noxious weeds thrive in water-conserving landscapes. The ability to identify local noxious weeds and how they spread is an important part of their control. Note that many common landscape plants are considered invasive or noxious in certain parts of the country.

Contact your local Cooperative Extension Service Office for more information on how to control these serious plant pests.
Additional Resources:
USDA Invasive and Noxious Weeds by state
Know the Weeds
Weed Identification Tools and Techniques
West
Alaska: BLM Alaska Weeds and Invasives Program
California: Invasive Weeds Resource List
Nevada: Fighting Invasive Weeds – A Northeastern Nevada Landowners’ Guide to Healthy Landscapes
Online Education Programs Weed Identification and Control videos
Southeast
Florida: Invasive Exotic Plants