In this review we will discuss the topic of high order harmonic generation (HHG) from samples of organic and bio-molecules. The possibility to extract useful dynamical and structural information from the measurement of the HHG emission, a technique termed high harmonic generation spectroscopy (HHGS), will be the special focus of our discussions. We will begin by introducing the salient facts of HHG from atoms and simple molecules and explaining the principles behind HHGS. Next the technical difficulties associated with HHG from samples of organic molecules and biomolecules, principally the low sample density and the low ionization potential, will be examined. Then we will present some recent experiments where HHG spectra from samples of these molecules have been measured and discuss what has been learned from these measurements. Finally we will look at the future prospects for HHG spectroscopy of organic molecules, discussing some of the technical and in principle limits of the technique and methods that may ameliorate these limits.