How do I use React and forms to get an array of checked checkbox values?

I am trying to build a filter for my portfolio website. Checkboxes that let you pick a technology (react, redux, jquery etc.) to display a piece of work(s) that contain(s) that/those technologies. So every time the user clicks on a box, I want to add the value (JavaScript, Redux, React etc.) to an array that I use in another function to check against my portfolio pieces and filter out what isn't there.

I am finding this very difficult and I think it should be quite simple. Can someone point me in the right direction? Is there a way to simply have a function trigger (onChange callback?) that reads the checked/unchecked status of my form input elements and then updates my state array accordingly? Can I get the status of all the checkboxes simply in React? Do I need to have individual state of checked/unchecked for my checkboxes?

It seems that jQuery makes it pretty possible with selectors with:

$('input[type="checkbox"]:checked').each(function () {}