Plastic packaging typically consists of a mixture of polymers and contains a whole range of components, such as paper, organic residue, halogens, and metals, which pose problems during recycling. Nevertheless, until today, limited detailed data are available on the full polymer composition of plastic packaging waste taking into account the separable packaging parts present in a certain waste stream, nor on their quantitative levels of (elemental) impurities. This paper therefore presents an unprecedented in-depth analysis of the polymer and elemental composition, including C, H, N, S, O, metals, and halogens, of commonly generated plastic packaging waste streams in European sorting facilities. Various analytical techniques are applied, including Fourier transform infrared (FTIR) spectroscopy, differential scanning calorimetry (DSC), polarized optical microscopy, ion chromatography, and inductively coupled plasma optical emission spectrometry (ICP-OES), on more than 100 different plastic packaging products, which are all separated into their different packaging subcomponents (e.g., a bottle into the bottle itself, the cap, and the label). Our results show that certain waste streams consist of mixtures of up to nine different polymers and contain various elements of the periodic table, in particular metals such as Ca, Al, Na, Zn, and Fe and halogens like Cl and F, occurring in concentrations between 1 and 3000 ppm. As discussed in the paper, both polymer and elemental impurities impede in many cases closed-loop recycling and require advanced pretreatment steps, increasing the overall recycling cost.