This introduction offers an overview of the chapters included in this book to highlight the connections between the different topics addressed. We clarify the different senses in which the objects dealt with in this volume can be regarded as special. The book begins by considering biochemical molecules as a kind of object that, even though it has a very specific material constitution with a defined structure, cannot be characterized solely in terms of it. The next contributions turn to objects that, although material, do not have a clearly constrained structure: artifacts may belong to the same kind despite having very dissimilar physical constitutions, and fictional entities may have different material engagement even if they perform the same narrative function. Then the book considers ontological issues regarding psychiatric and psychological kinds of objects, which have both physical and normative dimensions. The chapters progressively move away from these more material kinds towards the more immaterial realm of the social, the intentional and the notional, paying particular attention to the nature of fictional objects, until they reach the furthest limit in impossible and non-existent objects, raising questions about modality. The closing chapter puts the focus on metaphysical accounts of the remarkably special physical objects found in the quantum realm.