  We prove that if $T_1,\dots, T_n$ is a sequence of bounded degree trees so
that $T_i$ has $i$ vertices, then $K_n$ has a decomposition into $T_1,\dots,
T_n$. This shows that the tree packing conjecture of Gy\'arf\'as and Lehel from
1976 holds for all bounded degree trees (in fact, we can allow the first $o(n)$
trees to have arbitrary degrees). Similarly, we show that Ringel's conjecture
from 1963 holds for all bounded degree trees. We deduce these results from a
more general theorem, which yields decompositions of dense quasi-random graphs
into suitable families of bounded degree graphs. Our proofs involve
Szemer\'{e}di's regularity lemma, results on Hamilton decompositions of robust
expanders, random walks, iterative absorption as well as a recent blow-up lemma
for approximate decompositions.
