The COLORI proposal is devoted to the theoretical description, the numerical modeling, and the experimental study of cold and ultracold molecular collisions driven by long-range forces in the presence of strongly confining external potentials. The project brings together one theoretical and one experimental team. The coordinator IPR-Rennes has a strong theoretical background in the molecular dynamics field, the LENS-Florence partner is internationally recognized for its experimental contribution to the study of atomic and molecular gases in the ultracold domain. Experimental groups worldwide have developed the capability to cool and manipulate a large variety of atomic, molecular, and ionic species, forming the extremely active quantum gases community. Binary collisions occupy a pivotal position in the ultracold gas realm. It suffices to mention that the efficacity of cooling schemes and the quantum phases of an ultracold gas are controlled by two-body elastic and inelastic scattering amplitudes. The quantitative understanding of cold collisions is therefore essential to interpret ongoing experiments on quantum gases. Fortunately, cold collisions can not only be accurately understood, but even accurately controlled. External fields are the tool of choice, capable of influencing the outcome of a collision either by directly modifying the translational motion or by manipulating the internal structure of the colliding partners. Two main research topics can be identified in our proposal. The first one is a joint theoretical and experimental study of confinement effects on collisions of polar KRb bosonic molecules. The experimental developments ongoing at LENS include the set-up of an extremely stable laser system for two-photon transfer of weakly bound molecules to the absolute ground state. This study should allow us to shed light on the long-range interplay between dipolar, electric and optical forces, an extremely interesting topic in view of controlling unwanted reactive chemical processes expected to limit the gas lifetime. Confinement effects will be studied in particular in optical lattices of different dimensionality and crystal symmetry. We expect a wealth of geometric resonance phenomena and lattice-induced scattering events to be accurately described using the numerical tools developed during the project. Novel methodological and computational approaches will have to be proposed to this aim. Inclusion of hyperfine couplings in molecular collisions should allow novel resonance patterns and quantum interference phenomena to be studied. The second part of the COLORI proposal will consider atom-ion collisions in the presence of hyperfine and dynamical ion trap effects. Novel routes to collision control will be investigated by taking into account the interplay of resonances due to internal hyperfine couplings with Landau quantization of motional ion states in a magnetic field. Yet unexplored micromotion effects will be studied in collisions of atoms with ions trapped in Paul traps using both time-independent and time-dependent wavepacket methods. The realization of atom-ion quantum gates and sympathetic cooling of ions by ultracold atoms are only few examples for which a quantitative modeling of collisions is strongly needed. Finally, the numerical codes we propose to develop are expected to set a benchmark for theories based on effective and perturbative approaches to scattering in confined environments. COLORI presents a good equilibrium of scientific tasks between the IPR and LENS partners in the proposal, and between senior and young researchers. Periodic informal meetings are foreseen for coordination purposes. Publications in peer-reviewed journals and presentations in international meetings should help disseminating the main results of the present cooperative project.