Colloidal heteronanocrystals (HNCs) can be regarded as solution-grown inorganic-organic hybrid nanomaterials, since they consist of inorganic nanoparticles that are coated with a layer of organic ligand molecules. The hybrid nature of these nanostructures provides great flexibility in engineering their physical and chemical properties. The inorganic particles are heterostructured, i.e. they comprise two (or more) different materials joined together, what gives them remarkable and unique properties that can be controlled by the composition, size and shape of each component of the HNC. The interaction between the inorganic component and the organic ligand molecules allows the size and shape of the HNCs to be controlled and gives rise to novel properties. Moreover, the organic surfactant layer opens up the possibility of surface chemistry manipulation, making it possible to tailor a number of properties. These features have turned colloidal HNCs into promising materials for a number of applications, spurring a growing interest on the investigation of their preparation and properties. This critical review provides an overview of recent developments in this rapidly expanding field, with emphasis on semiconductor HNCs (e.g., quantum dots and quantum rods). In addition to defining the state of the art and highlighting the key issues in the field, this review addresses the fundamental physical and chemical principles needed to understand the properties and preparation of colloidal HNCs (283 references).