We focus on reviewing state-of-the-art developments of dedicated PET scanners with irregular geometries and the potential of different aspects of multifunctional PET imaging. First, we discuss advances in non-conventional PET detector geometries. Then, we present innovative designs of organ-specific dedicated PET scanners for breast, brain, prostate, and cardiac imaging. We will also review challenges and possible artifacts by image reconstruction algorithms for PET scanners with irregular geometries, such as non-cylindrical and partial angular coverage geometries and how they can be addressed. Then, we attempt to address some open issues about cost/benefits analysis of dedicated PET scanners, how far are the theoretical conceptual designs from the market/clinic, and strategies to reduce fabrication cost without compromising performance.