diff --git a/configure.ac b/configure.ac
index e89ed1d..680dde7 100644
--- a/configure.ac
+++ b/configure.ac
@@ -249,6 +249,8 @@ TAR_COMPR_PROGRAM(bzip2)
 TAR_COMPR_PROGRAM(lzip)
 TAR_COMPR_PROGRAM(lzma)
 TAR_COMPR_PROGRAM(lzop)
+TAR_COMPR_PROGRAM(lz4)
+TAR_COMPR_PROGRAM(zstd)
 TAR_COMPR_PROGRAM(xz)
 
 AC_MSG_CHECKING(for default archive format)
diff --git a/doc/tar.1 b/doc/tar.1
index f5c1fca..3506169 100644
--- a/doc/tar.1
+++ b/doc/tar.1
@@ -13,7 +13,7 @@
 .\"
 .\" You should have received a copy of the GNU General Public License
 .\" along with this program.  If not, see <http://www.gnu.org/licenses/>.
-.TH TAR 1 "March 23, 2016" "TAR" "GNU TAR Manual"
+.TH TAR 1 "August 5, 2017" "TAR" "GNU TAR Manual"
 .SH NAME
 tar \- an archiving utility
 .SH SYNOPSIS
@@ -818,6 +818,14 @@ Filter the archive through
 Filter the archive through
 .BR lzop (1).
 .TP
+\fB\-\-lz4\fR
+Filter the archive through
+.BR lz4 (1).
+.TP
+\fB\-\-zstd\fR
+Filter the archive through
+.BR zstd (1).
+.TP
 \fB\-\-no\-auto\-compress\fR
 Do not use archive suffix to determine the compression program.
 .TP
@@ -1285,6 +1293,8 @@ failure during backup to a remote device.
 .BR gzip (1),
 .BR lzma (1),
 .BR lzop (1),
+.BR lz4 (1),
+.BR zstd (1),
 .BR rmt (8),
 .BR symlink (7),
 .BR tar (5),
diff --git a/doc/tar.texi b/doc/tar.texi
index edd190e..1ac1d4b 100644
--- a/doc/tar.texi
+++ b/doc/tar.texi
@@ -2971,6 +2971,16 @@ This option tells @command{tar} to read or write archives through
 This option tells @command{tar} to read or write archives through
 @command{lzop}.  @xref{gzip}.
 
address@hidden --lz4
+
+This option tells @command{tar} to read or write archives through
address@hidden  @xref{gzip}.
+
address@hidden --zstd
+
+This option tells @command{tar} to read or write archives through
address@hidden  @xref{gzip}.
+
 @opsummary{mode}
 @item address@hidden
 
@@ -9568,14 +9578,17 @@ switch to @samp{posix}.
 @cindex lzip
 @cindex lzma
 @cindex lzop
address@hidden lz4
address@hidden zstd
 @cindex compress
 @GNUTAR{} is able to create and read compressed archives.  It supports
 a wide variety of compression programs, namely: @command{gzip},
 @command{bzip2}, @command{lzip}, @command{lzma}, @command{lzop},
address@hidden and traditional @command{compress}. The latter is
-supported mostly for backward compatibility, and we recommend
-against using it, because it is by far less effective than the other
-compression address@hidden also had patent problems in the past.}.
address@hidden, @command{zstd}, @command{xz} and traditional
address@hidden  The latter is supported mostly for backward
+compatibility, and we recommend against using it, because it is by far
+less effective than the other compression address@hidden also
+had patent problems in the past.}.
 
 Creating a compressed archive is simple: you just specify a
 @dfn{compression option} along with the usual archive creation
@@ -9584,10 +9597,11 @@ create a @command{gzip} compressed archive, @option{-j}
 (@option{--bzip2}) to create a @command{bzip2} compressed archive,
 @option{--lzip} to create an @asis{lzip} compressed archive,
 @option{-J} (@option{--xz}) to create an @asis{XZ} archive,
address@hidden to create an @asis{LZMA} compressed
-archive, @option{--lzop} to create an @asis{LSOP} archive, and
address@hidden (@option{--compress}) to use @command{compress} program.
-For example:
address@hidden to create an @asis{LZMA} compressed archive,
address@hidden to create an @asis{LSOP} archive, @option{--lz4} to
+create an @asis{LZ4} archive, @option{--zstd} to create an @asis{ZST}
+archive, and @option{-Z} (@option{--compress}) to use
address@hidden program.  For example:
 
 @smallexample
 $ @kbd{tar czf archive.tar.gz .}
@@ -9707,6 +9721,14 @@ Filter the archive through @command{lzma}.
 @item --lzop
 Filter the archive through @command{lzop}.
 
address@hidden lz4
address@hidden --lz4
+Filter the archive through @command{lz4}.
+
address@hidden zstd
address@hidden --zstd
+Filter the archive through @command{zstd}.
+
 @opindex compress
 @opindex uncompress
 @item -Z
@@ -9778,6 +9800,8 @@ suffix.  The following suffixes are recognized:
 @item @samp{.lzma} @tab @command{lzma}
 @item @samp{.tlz} @tab @command{lzma}
 @item @samp{.lzo} @tab @command{lzop}
address@hidden @samp{.lz4} @tab @command{lz4}
address@hidden @samp{.zst} @tab @command{zstd}
 @item @samp{.xz} @tab @command{xz}
 @end multitable
 
diff --git a/src/buffer.c b/src/buffer.c
index 6f96c2f..d635499 100644
--- a/src/buffer.c
+++ b/src/buffer.c
@@ -281,6 +281,8 @@ enum compress_type {
   ct_lzip,
   ct_lzma,
   ct_lzop,
+  ct_lz4,
+  ct_zstd,
   ct_xz
 };
 
@@ -309,6 +311,8 @@ static struct zip_magic const magic[] = {
   { ct_lzip,     4, "LZIP" },
   { ct_lzma,     6, "\xFFLZMA" },
   { ct_lzop,     4, "\211LZO" },
+  { ct_lz4,      4, "\x04\x22\x4D\x18" },
+  { ct_zstd,     4, "\x28\xB5\x2F\xFD" },
   { ct_xz,       6, "\xFD" "7zXZ" },
 };
 
@@ -324,6 +328,8 @@ static struct zip_program zip_program[] = {
   { ct_lzma,     LZMA_PROGRAM,     "--lzma" },
   { ct_lzma,     XZ_PROGRAM,       "-J" },
   { ct_lzop,     LZOP_PROGRAM,     "--lzop" },
+  { ct_lz4,      LZ4_PROGRAM,      "--lz4" },
+  { ct_zstd,     ZSTD_PROGRAM,     "--zstd" },
   { ct_xz,       XZ_PROGRAM,       "-J" },
   { ct_none }
 };
diff --git a/src/suffix.c b/src/suffix.c
index 47027e7..251a3ae 100644
--- a/src/suffix.c
+++ b/src/suffix.c
@@ -44,6 +44,8 @@ static struct compression_suffix compression_suffixes[] = {
   { S(lzma, LZMA) },
   { S(tlz,  LZMA) },
   { S(lzo,  LZOP) },
+  { S(lz4,  LZ4) },
+  { S(zst,  ZSTD) },
   { S(xz,   XZ) },
   { S(txz,  XZ) }, /* Slackware */
   { NULL }
diff --git a/src/tar.c b/src/tar.c
index ea68c82..74b8a6e 100644
--- a/src/tar.c
+++ b/src/tar.c
@@ -293,6 +293,8 @@ enum
   LZIP_OPTION,
   LZMA_OPTION,
   LZOP_OPTION,
+  LZ4_OPTION,
+  ZSTD_OPTION,
   MODE_OPTION,
   MTIME_OPTION,
   NEWER_MTIME_OPTION,
@@ -681,6 +683,8 @@ static struct argp_option options[] = {
   {"lzip", LZIP_OPTION, 0, 0, NULL, GRID+1 },
   {"lzma", LZMA_OPTION, 0, 0, NULL, GRID+1 },
   {"lzop", LZOP_OPTION, 0, 0, NULL, GRID+1 },
+  {"lz4", LZ4_OPTION, 0, 0, NULL, GRID+1 },
+  {"zstd", ZSTD_OPTION, 0, 0, NULL, GRID+1 },
   {"xz", 'J', 0, 0, NULL, GRID+1 },
 #undef GRID
 
@@ -1123,6 +1127,15 @@ tar_help_filter (int key, const char *text, void *input)
 
     case LZOP_OPTION:
       s = xasprintf (_("filter the archive through %s"), LZOP_PROGRAM);
+      break;
+
+    case LZ4_OPTION:
+      s = xasprintf (_("filter the archive through %s"), LZ4_PROGRAM);
+      break;
+
+    case ZSTD_OPTION:
+      s = xasprintf (_("filter the archive through %s"), ZSTD_PROGRAM);
+      break;
 
     case 'J':
       s = xasprintf (_("filter the archive through %s"), XZ_PROGRAM);
@@ -1494,6 +1507,14 @@ parse_opt (int key, char *arg, struct argp_state *state)
       set_use_compress_program_option (LZOP_PROGRAM, args->loc);
       break;
 
+    case LZ4_OPTION:
+      set_use_compress_program_option (LZ4_PROGRAM, args->loc);
+      break;
+
+    case ZSTD_OPTION:
+      set_use_compress_program_option (ZSTD_PROGRAM, args->loc);
+      break;
+
     case 'm':
       touch_option = true;
       break;