Respiratory motion has been found to degrade the image quality in many clinical PET studies, and more recently SPECT studies with a high-resolution semiconductor-based SPECT camera. Currently in the image generation and/or reconstruction field for tomography, including PET, SPECT and X-ray CT, respiratory motion compensation is a hot topic which attracts significant interest and attention. During the 2013 IEEE NSS/MIC/RTSD conference just held in Seoul, Korea, there was a special workshop focusing on the four dimensional quantitative image reconstruction topics, among  which respiratory motion compensation took an important part.  The fact that image degradation induced by respiratory motion is more related to patients’ physiology rather than radiation physics ，makes it perhaps even more difficult than attenuation and scatter compensation in ECT imaging. Partial volume compensation is another important research topic in PET and SPECT imaging; given that SPECT/CT, PET/CT and PET/MR multi-modality integrated scanners are widely available in clinics nowadays. With CT or MR based anatomic prior information, it has been shown that partial volume compensation can significantly improve the image resolution of PET or SPECT without amplifying image noise. In this seminar, we will discuss a few recently developed algorithms including an event-by-event respiratory motion correction method for irregular breathing pattern patients and  a partial volume correction method for low counts data. We will focus on the applications of pancreas PET imaging and cardiac SPECT imaging.