I understand the chemical herbicide, "Round-Up," is coming under close scrutiny.  Reports are its use is banned in Europe and there have been jury awards for negative health effects in California.

I have been advised to treat invasive shrubs such as Asian Honeysuckle and Russian Olive but do not want to create a legacy similar to "Agent Orange." 

Is "Round Up" recommended? If not, are there safer chemicals?  Other choices short of lots of digging and pulling over grown shrubs.

Thanks