Keeping it short, I'm trying to accomplish the way https://artsy.net/browse/artworks? stacks their thumbs.

I've going crazy trying different things with bootstrap 3. But I'm starting to think that this has to be done with JS (??).

My first choice is to use a pre made jQuery plugin, but haven't found any.

Maybe I'm going blind now after many tries. I'm not asking for the exact solution, I just need some pointers as to what to look into or search for.

I'd start with a search for "Bootstrap Thumbnail Grid".

To get you started, .thumbnail > img will cause the image to take up 100% of it's placeholder.
If you put the thumbnails inside of responsive columns with the same width, they should line up:

<!-- language: lang-html -->
<div class="row">
    <div class="col-xs-3">
        <a href="#" class="thumbnail">
        <img src="http://placehold.it/400x200" alt="..." />
        </a>
    </div>
    <div class="col-xs-3">
         <a href="#" class="thumbnail">
        <img src="http://placehold.it/300x150" alt="..." />
        </a>
    </div>
    <!-- More columns -->
</div>

##Working demo in jsFiddle

screenshot