Shining light through walls? At first glance this sounds crazy. However, very feeble gravitational and electroweak effects allow for this exotic possibility. Unfortunately, with present and near future technologies the opportunity to observe light shining through walls via these effects is completely out of the question. Nevertheless, there are quite a number of experimental collaborations around the globe involved in this quest. Why are they doing it? Are there additional ways of sending photons through opaque matter? Indeed, various extensions of the standard model of particle physics predict the existence of new particles called WISPs - extremely weakly interacting slim particles. Photons can convert into these hypothetical particles, which have no problems to penetrate very dense materials, and these can reconvert into photons after their passage - as if light was effectively traversing walls. We review this exciting field of research, describing the most important WISPs, the present and future experiments, the indirect hints from astrophysics and cosmology pointing to the existence of WISPs, and finally outlining the consequences that the discovery of WISPs would have.