The ones on the broccoli are cabbage loopers, you just have to pick htem off as you find them or they will eat your broccoli and broccoli leaves.
We pick them off and drop t hem into a cup of alcohol.

Well, most gardeners want to have host plants for the swallowtail butterfly caterpillars. Next year plant some bronze fennel near your garden and they'll go to that instead.

As for your broccoli, you've just discovered why many gardeners quit growing broccoli altogether. What has finally worked for me is having a mature perennial garden that attracts beneficial insects which eat the "bad guys". This is the first year I had no problem with the loopers so I'll probably try for a fall planting of broccoli now.

Pest management is complex, if you wish to use chemical products, do so responsibly which goes further than reading the label. If you want to learn, a good place to start is here:

Integrated Pest Management
This lecture is presented in two parts. Each part is 90-minutes in length. Recorded in Sacramento County in California's Sacramento Valley, this lecture is by Mary Louise Flint, Ph.D., Director, IPM Education and Publications, UC Statewide IPM Project and Extension Entomologist & Cooperative Extension Specialist.

Education:
B.S. Plant Science, University of California, Davis
Ph.D. Entomology, University of California, Berkeley

Appointment:
100% Cooperative Extension

Research Interests:
Integrated pest management of landscape, agricultural and garden pests; biological control of arthropod pests; alternatives to pesticides; adoption of alternative practices by practitioners; innovative delivery of pest management information.

Topics discussed in the Integrated Pest Management Lecture:

* IPM references and resources
* Preventing pest problems
* Natural common enemies
* Making less toxic pesticide choices
* Controlling aphids, scales, caterpillars, coddling moths, tree borers, snails and slugs, and lawn insects.

You can watch the programs now online:

Just make sure you have Real Player installed or download it free.

Integrated Pest Management Part1 90 minutes

Integrated Pest Management Part 2 90 minutes

You'll want to bookmark the following link to Professor Flint's Lab Research on:
Controlling Pests in Gardens and Landscapes: Vegetables and Melons

I promise you'll learn one or two things to put in your gardening bag of pest management arsenals.

;)

Here is a link that might be useful: Cabbage Looper Management