Title: The nature of the polymer collapse transition                                                                                                                                                                                                                                                                                                                                        Abstract: In a good solvent, a polymer chain assumes an extended configuration. Asthe solvent quality (or the temperature) is lowered, the configuration changes to globular, which is more compact. This collapse transition is also called coil-globule transition in the literature. Since the pioneering work by de Gennes, it is known that it corresponds to a tricritical point in a grand-canonical parameter space. In the most used lattice model to study it, the chain is represented by a self-avoiding walk on the lattice and the solvent is effectively taken into account by including attractive interactions between monomers on first neighbor sites which are not consecutive along a chain (SASAW's: self-attracting self-avoiding walks). We will review the model and show that small changes in it may lead to different phase diagrams, where the collapse transition is no longer a tricritial point. In particular, if the polymer is represented by a trail, which allows for multiple visits of sites but mantains the constraint of single visits of edges, we find two distinct polymerized phases besides the non-polymerized phase and the collapse transition becomes a bicritical point.