In many REST frameworks calling the HTTP PUT or DELETE operations from a browser can be achieved through what is known as an "Overloaded POST". What this means is you submit the request from the browser to the server as a POST request with some information appended to the URL specifying the actual HTTP method that should be used.
I know that the Restlet framework for Java follows this approach and I believe Rails does as well.
So if you have a REST API defineed like this:
POST - http://myservice/myobject -> creates a new object and
returns the object id
GET - http://myservice/myobject/id ->
returns the object
PUT - http://myservice/myobject/id ->
updates the object
DELETE - http://myservice/myobject/id ->
deletes the object
using Overloaded POST from the browser you could also
POST - http://myservice/myobject/id?method=PUT -> updates the object
POST - http://myservice/myobject/id?method=DELETE -> deletes the object
In fact, for Flex which does not support PUT or DELETE, this is the only way to call these REST operations.