Transposable elements (TEs) are major components of large plant genomes and main drivers of genome evolution. The most recent assembly of hexaploid bread wheat recovered the highly repetitive TE space in an almost complete chromosomal context and enabled a detailed view into the dynamics of TEs in the A, B, and D subgenomes. The overall TE content is very similar between the A, B, and D subgenomes, although we find no evidence for bursts of TE amplification after the polyploidization events. Despite the near-complete turnover of TEs since the subgenome lineages diverged from a common ancestor, 76% of TE families are still present in similar proportions in each subgenome. Moreover, spacing between syntenic genes is also conserved, even though syntenic TEs have been replaced by new insertions over time, suggesting that distances between genes, but not sequences, are under evolutionary constraints. The TE composition of the immediate gene vicinity differs from the core intergenic regions. We find the same TE families to be enriched or depleted near genes in all three subgenomes. Evaluations at the subfamily level of timed long terminal repeat-retrotransposon insertions highlight the independent evolution of the diploid A, B, and D lineages before polyploidization and cases of concerted proliferation in the AB tetraploid. Even though the intergenic space is changed by the TE turnover, an unexpected preservation is observed between the A, B, and D subgenomes for features like TE family proportions, gene spacing, and TE enrichment near genes.