Discrete　breathers　(DBs),　also　known　as　intrinsic　localized　modes,　are　spatially　localized　nonlinear　vibrational　modes　in　defected-free　anharmonic　lattices　and　expected　to　affect　energy　transfer　process.　However,　whether　DBs　can　contribute　to　thermal　transport　at　finite　temperature　is　still　not　very　clear.　In　the　present　work,　we　briefly　describe　our　recent　results　on　the　possible　effects　of　DBs　on　heat　transport.　By　employing　two　one-dimensional　(1D)　anharmonic　lattice　models　with　different　phonon　dispersions,　we　provide　some　numerical　evidences　to　demonstrate　that　given　the　peculiar　phonon　dispersions　along　with　nonlinearity,　two　kinds　of　DBs,　i.e.,　the　intra-band　and　extra-band　ones,　can　exist　in　1D　lattices　at　finite　temperature　and　thus　contribute　to　thermal　transport　in　different　ways,　i.e.,　the　intra-band　DBs　can　be　scattering　with　phonons;　while　the　extra-band　DBs　mainly　localize　the　system　energies,　thus　both　tend　to　limit　the　heat　transport　in　the　thermodynamic　limit.　Our　results　here　suggest　that　different　peculiar　phonon　dispersions　along　with　nonlinearity　can　enable　us　to　excite　different　types　of　DBs,　which　then　affect　the　heat　transport　process　in　different　ways.　These　results　may　provide　useful　information　for　establishing　the　connection　between　the　macroscopic　heat　transport　process　and　the　underlying　DBs　dynamics　in　general　1D　nonlinear　systems　with　various　phonon　dispersions.　©　2016,　Institute　for　Metals　Superplasticity　Problems　of　Russian　Academy　of　Sciences.　All　rights　reserved.