Positron emission tomography (PET), intrinsically a 3D imaging technique, was for a long time exclusively operated in 2D mode, using septa to shield the detectors from photons emitted obliquely to the detector planes. However, the use of septa results in a considerable loss of sensitivity. From the late 1980s, significant efforts have been made to develop a methodology for the acquisition and reconstruction of 3D PET data. This paper focuses on the differences between data acquisition in 2D and 3D mode, especially in terms of data set sizes and representation. Although the real time data acquisition aspect in 3D has been mostly solved in modern PET scanner systems, there still remain questions on how to represent and how to make best use of the information contained in the acquired data sets. Data representation methods, such as list-mode and matrix-based methods, possibly with additional compression, will be discussed. Moving from 2D to 3D PET has major implications on the way these data are reconstructed to images. Two fundamentally different approaches exist, the analytical one and the iterative one. Both, at different expenses, can be extended to directly handle 3D data sets. Either way the computational burden increases heavily compared to 2D reconstruction. One possibility to benefit from the increased sensitivity in 3D PET while sticking to high-performance 2D reconstruction algorithms is to rebin 3D into 2D data sets. The value of data rebinning will be explored. An ever increasing computing power and the concept of distributed or parallel computing have made direct 3D reconstruction feasible. Following a short review of reconstruction methods and their extensions to 3D, we focus on numerical aspects that improve reconstruction performance, which is especially important in solving large equation systems in 3D iterative reconstruction. Finally exemplary results are shown to review the properties of the discussed algorithms. This paper concludes with an overview on future trends in data representation and reconstruction.