On the DJ Vadim website I needed to create a gallery of album covers that displayed each cover in a perfect square, but was also responsive and would resize dynamically on various screen sizes. I could have declared a whole variety of CSS values for each media breakpoint, but I wanted a much more elegant solution. I settled on the following:
Check the J Fiddle
The solution is to give the containing hyperlink for each thumbnail a width off 100%, and a height of 0. The square is calculated by a bottom padding of 100%. The image itself is applied as a background image to the hyperlink, and sized using the CSS property background-size.