Why do we see certain types of strongly interacting elementary particles and not others? This question was posed over 50 years ago in the context of the quark model. M. Gell-Mann and G. Zweig proposed that the known mesons were $q bar q$ and baryons $qqq$, with quarks known at the time $u$ (up), $d$ (down), and $s$ (strange) having charges (2/3,-1/3,-1/3). Mesons and baryons would then have integral charges. Mesons such as $qq bar q bar q$ and baryons such as $qqqq bar q$ would also have integral charges. Why werent they seen? They have now been seen, but only with additional heavy quarks and under conditions which tell us a lot about the strong interactions and how they manifest themselves. The present article describes recent progress in our understanding of such exotic mesons and baryons.