I've already done my research, but didn't found an exact solution (if I can call it like that) to my problem.
So basically what I do? - I'm sending a AJAX (a default jQuery $.ajax) request to the page I'm currently and when I get $(response) I want to replace only the contents that are different and to ?re-activate? the JS events for them.
I will share with you an example that I have in mind, may be will clear out my question.
I want something like this:
for(response.differences in d) {
$("body").find(d.element).replace(d.html);
}
//now re-activate; re-init the JS for the new content somehow