It takes time to figure out how to successfully fight back against insect invaders. They're much more difficult to contain than mammals, and it typically takes a multi-prong attack to get a place back into balance once an aggressive invasive has been introduced.
That doesn't mean you can't suppress them. The gypsy moth was first introduced to America in 1869 in MA. Through serious concentrated work (for over a century!), the moths' progression across the U.S. has been restricted. Unfortunately, invaded areas typically are defoliated.
The Longhorned Eucalyptus Borer, another introduced pest, currently has limited range, but that's mostly due to geography. The insects typically live in mediterranean climates. Their range currently includes CA, AZ, and parts of British Columbia. In an effort to battle the borers, their natural enemies were introduced to infested areas. So, now there are parasitic wasps to control the beetles living where the beetles live. This is not an unusual tactic.
In parts of Southern California, some snails in your garden may have shells that look a little odd. Don't kill them - they're there to help you. They're called "decollate snails" and are snails that snack on other snails. http://www.ipm.ucdavis.edu/PMG/NE/decollate_snail.html
Another way to control the spread of pests is through quarantine. Thanks to the Asian Citrus Psyllid, there are currently quarantines on on some citrus within California. The quarantine is necessary. The insect doesn't just feed on citrus, it's a disease vector. When an Asian Citrus Psyllid feeds on a tree, it can transmit Citrus Greening disease, Huanglongbing (HLB), and that can kill the tree. The quarantine is a needed precaution.