The Site Frequency Spectrum (SFS) and the heterozygosity of allelic variants are among the most important summary statistics for population genetic analysis of diploid organisms. We discuss the generalisation of these statistics to populations of autopolyploid organisms in terms of the joint Site Frequency/Dosage Spectrum and its expected value for autopolyploid populations that follow the standard neutral model. Based on these results, we present estimators of nucleotide variability from High-Throughput Sequencing (HTS) data of autopolyploids and discuss potential issues related to sequencing errors and variant calling. We use these estimators to generalise Tajima's D and other SFS-based neutrality tests to HTS data from autopolyploid organisms. Finally, we discuss how these approaches fail when the number of individuals is small. In fact, in autopolyploids there are many possible deviations from the Hardy-Weinberg equilibrium, each reflected in a different shape of the individual dosage distribution. The SFS from small samples is often dominated by the shape of these deviations of the dosage distribution from its Hardy-Weinberg expectations.