Transposable elements (TEs) are the main components of genomes. However, due to their repetitive nature, they are very difficult to study using data obtained with short-read sequencing technologies. Here, we describe an efficient pipeline to accurately recover TE insertion (TEI) sites and sequences from long reads obtained by Oxford Nanopore Technology (ONT) sequencing. With this pipeline, we could precisely describe the landscapes of the most recent TEIs in wild-type strains of Drosophila melanogaster and Drosophila simulans. Their comparison suggests that this subset of TE sequences is more similar than previously thought in these two species. The chromosome assemblies obtained using this pipeline also allowed recovering piRNA cluster sequences, which was impossible using short-read sequencing. Finally, we used our pipeline to analyze ONT sequencing data from a D. melanogaster unstable line in which LTR transposition was derepressed for 73 successive generations. We could rely on single reads to identify new insertions with intact target site duplications. Moreover, the detailed analysis of TEIs in the wild-type strains and the unstable line did not support the trap model claiming that piRNA clusters are hotspots of TE insertions.