The aim of this thesis is to design, implement, and evaluate respiratory motion correction techniques that can overcome respiratory motion artifacts in PET/CT imaging. The thesis is composed of three main sections. The first section introduces a novel approach (free-breathing amplitude gating (FBAG) technique) to correct for respiratory motion artifacts. This approach is based on sorting the acquired PET data in multiple amplitude bins which is currently not possible on any commercial PET/CT scanner. The second section is focused on the hardware/software design of an in-house respiratory gating device that is necessary to facilitate the implementation of the FBAG technique. Currently there are no commercially available respiratory gating systems that can generate the necessary triggers required for the FBAG technique. The third section is focused on developing a joint correction technique that can simultaneously suppress respiratory motion artifacts as well as partial volume effects (PVE) which represent another source of image degradation in PET/CT imaging. Computer simulations, phantom studies, as well as patient studies are conducted to test the performance of these proposed techniques and their results are shown in this thesis.