The rapid expansion of machine learning is offering a new wave of opportunities for nuclear medicine. This paper reviews applications of machine learning for the study of attenuation correction (AC) and low-count image reconstruction in quantitative positron emission tomography (PET). Specifically, we present the developments of machine learning methodology, ranging from random forest and dictionary learning to the latest convolutional neural network-based architectures. For application in PET attenuation correction, two general strategies are reviewed: 1) generating synthetic CT from MR or non-AC PET for the purposes of PET AC, and 2) direct conversion from non-AC PET to AC PET. For low-count PET reconstruction, recent deep learning-based studies and the potential advantages over conventional machine learning-based methods are presented and discussed. In each application, the proposed methods, study designs and performance of published studies are listed and compared with a brief discussion. Finally, the overall contributions and remaining challenges are summarized.