There are many questions surrounding the need and effectiveness of invasive plant management, particularly the methods used. Fortunately, there have been many educational resources developed to explore these topics. Below are links to some of these educational materials.
The California Invasive Plant Council (Cal-IPC) is a great place to start learning about invasive plants and their impacts on natural and human systems. (Start with the definitions and impacts pages.)
The University of California some great information about invasive weeds, and what management techniques are effective. The Weed Research and Information Center and the University of California Integrated Pest Management (UC IPM) websites are great resources for information about invasive agricultural and urban weeds.
As seen in the picture below, if left unchecked, invasive weeds can create monocultures, reducing biodiversity: