life cycle of search and filter related to model

i been trying to search about a life cycle of search and filter but i couldn’t found any thing , i hope some one can please exactly explain how the search method takes to previous criteria ?

For an example a user perform a search and then some advance search so if i use filters outside of the div , widget or on a sidebar as a portlet , what i understand is i will have to set the value in search function but what about the previous search criteria ? as i might be only setting one value for comparison ?

Thanks