We will study how vibrational properties of nanobridges can be tuned through temperature and mechanical stress. Developing an ab-initio description based on density functional theory, we will include anharmonic effects to consider their influence on the heat current by phonons and its fluctuations. Within this methodology that allows to determine phonon lifetimes based on phonon-phonon scattering, we will focus on molecular and atomic scale junctions. We will explore the dependence of phonon transport on molecular shape, conjugation, anchoring groups, substituents and electrode materials as well as ways to achieve a suppression of thermal conductance through destructive phonon interference and increased anharmonicities. Finally, using molecular dynamics and force fields, calibrated with the ab-initio approach, we will explore a new type of thermal diode that exploits different thermal expansion coefficients to achieve a high rectification ratio.