diff --git a/Doc/library/lzma.rst b/Doc/library/lzma.rst
index 69f7cb8d48d7ae..deec54fad9ed32 100644
--- a/Doc/library/lzma.rst
+++ b/Doc/library/lzma.rst
@@ -336,6 +336,39 @@ Miscellaneous
    feature set.
 
 
+Information about the version of the lzma library in use is available through
+the following constants:
+
+
+.. data:: LZMA_VERSION
+.. data:: LZMA_VERSION_STRING
+
+   The version of the lzma C library actually loaded at runtime, in both
+   integer and string forms.
+
+   .. versionadded:: 3.15
+
+.. data:: LZMA_HEADER_VERSION
+.. data:: LZMA_HEADER_VERSION_STRING
+
+   The version of the lzma library that was used for building the module, in
+   both integer and string forms.  This may be different from the lzma library
+   actually used at runtime.
+
+   .. versionadded:: 3.15
+
+The version number and string formats are as defined in by C library. The
+integer is represented in decimal digits as ``jmmmppps`` where ``j`` is the
+major version, ``mmm`` is the minor version, ``ppp`` is the patch level, and
+``s`` is the "stability indicator" (2 means stable)::
+
+   >>> import lzma
+   >>> lzma.LZMA_VERSION
+   50020052
+   >>> lzma.LZMA_VERSION_STRING
+   '5.2.5'
+
+
 .. _filter-chain-specs:
 
 Specifying custom filter chains
@@ -357,12 +390,26 @@ options. Valid filter IDs are as follows:
 
 * Branch-Call-Jump (BCJ) filters:
 
-  * :const:`FILTER_X86`
-  * :const:`FILTER_IA64`
-  * :const:`FILTER_ARM`
-  * :const:`FILTER_ARMTHUMB`
-  * :const:`FILTER_POWERPC`
-  * :const:`FILTER_SPARC`
+  * :const:`!FILTER_X86`
+  * :const:`!FILTER_IA64`
+  * :const:`!FILTER_ARM`
+  * :const:`!FILTER_ARMTHUMB`
+  * :const:`!FILTER_POWERPC`
+  * :const:`!FILTER_SPARC`
+
+    The above work on all lzma runtime library versions.
+
+  * :const:`!FILTER_ARM64`
+
+    Only works if the lzma version is 5.4.0 or later.
+
+    .. versionadded:: 3.15
+
+  * :const:`!FILTER_RISCV`
+
+    Only works if the lzma version is 5.6.0 or later.
+
+    .. versionadded:: 3.15
 
 A filter chain can consist of up to 4 filters, and cannot be empty. The last
 filter in the chain must be a compression filter, and any other filters must be
diff --git a/Doc/whatsnew/3.15.rst b/Doc/whatsnew/3.15.rst
index 010abb7d9b9278..7533f62e54ab1d 100644
--- a/Doc/whatsnew/3.15.rst
+++ b/Doc/whatsnew/3.15.rst
@@ -206,6 +206,21 @@ difflib
   (Contributed by Jiahao Li in :gh:`134580`.)
 
 
+lzma
+----
+
+* Add :const:`lzma.LZMA_VERSION`, :const:`lzma.LZMA_HEADER_VERSION`, and
+  related constants. They report the version of the underlying ``lzma`` library
+  found at runtime and the header versions used at build time.
+  (Contributed by Chien Wong in :gh:`115988`.)
+
+* Add support of new BCJ filters ARM64 and RISC-V via
+  :const:`!lzma.FILTER_ARM64` and :const:`!lzma.FILTER_RISCV`.  Note that the
+  new filters will work only if runtime library supports them. ARM64 filter
+  requires ``lzma`` 5.4.0 or newer while RISC-V requires 5.6.0 or newer.
+  (Contributed by Chien Wong in :gh:`115988`.)
+
+
 math
 ----
 
diff --git a/Lib/lzma.py b/Lib/lzma.py
index 316066d024ea02..5f44a43224baa3 100644
--- a/Lib/lzma.py
+++ b/Lib/lzma.py
@@ -13,7 +13,10 @@
     "CHECK_ID_MAX", "CHECK_UNKNOWN",
     "FILTER_LZMA1", "FILTER_LZMA2", "FILTER_DELTA", "FILTER_X86", "FILTER_IA64",
     "FILTER_ARM", "FILTER_ARMTHUMB", "FILTER_POWERPC", "FILTER_SPARC",
+    "FILTER_ARM64", "FILTER_RISCV",
     "FORMAT_AUTO", "FORMAT_XZ", "FORMAT_ALONE", "FORMAT_RAW",
+    "LZMA_HEADER_VERSION", "LZMA_HEADER_VERSION_STRING",
+    "LZMA_VERSION", "LZMA_VERSION_STRING",
     "MF_HC3", "MF_HC4", "MF_BT2", "MF_BT3", "MF_BT4",
     "MODE_FAST", "MODE_NORMAL", "PRESET_DEFAULT", "PRESET_EXTREME",
 
diff --git a/Lib/test/test_lzma.py b/Lib/test/test_lzma.py
index e93c3c37354e27..fca852dcd4faa9 100644
--- a/Lib/test/test_lzma.py
+++ b/Lib/test/test_lzma.py
@@ -383,6 +383,20 @@ def test_uninitialized_LZMADecompressor_crash(self):
         self.assertEqual(LZMADecompressor.__new__(LZMADecompressor).
                          decompress(bytes()), b'')
 
+    def test_riscv_filter_constant_exists(self):
+        self.assertTrue(lzma.FILTER_RISCV)
+
+    def test_arm64_filter_constant_exists(self):
+        self.assertTrue(lzma.FILTER_ARM64)
+
+    def test_lzma_header_versions(self):
+        self.assertIsInstance(lzma.LZMA_HEADER_VERSION_STRING, str)
+        self.assertGreater(lzma.LZMA_HEADER_VERSION, 0)
+
+    def test_lzma_versions(self):
+        self.assertIsInstance(lzma.LZMA_VERSION_STRING, str)
+        self.assertGreater(lzma.LZMA_VERSION, 0)
+
 
 class CompressDecompressFunctionTestCase(unittest.TestCase):
 
diff --git a/Misc/NEWS.d/next/Library/2024-03-17-22-16-53.gh-issue-115988.EshSDM.rst b/Misc/NEWS.d/next/Library/2024-03-17-22-16-53.gh-issue-115988.EshSDM.rst
new file mode 100644
index 00000000000000..e0d18a88d49d8b
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2024-03-17-22-16-53.gh-issue-115988.EshSDM.rst
@@ -0,0 +1,2 @@
+:mod:`lzma` gains C library version info constants and adds constants to
+support the newer BCJ filters for ARM64 and RISC-V.
diff --git a/Modules/_lzmamodule.c b/Modules/_lzmamodule.c
index 462c2181fa6036..a5ffb3996c3477 100644
--- a/Modules/_lzmamodule.c
+++ b/Modules/_lzmamodule.c
@@ -25,6 +25,19 @@
     #error "The maximum block size accepted by liblzma is SIZE_MAX."
 #endif
 
+
+/*
+ * If the lzma.h we're building against is so old as not to define these, this
+ * provides their equivalent values so that the names remain defined in Python
+ * regardless of the header versions used at build time.
+ */
+#ifndef LZMA_FILTER_ARM64
+#define LZMA_FILTER_ARM64       LZMA_VLI_C(0x0A)
+#endif
+#ifndef LZMA_FILTER_RISCV
+#define LZMA_FILTER_RISCV       LZMA_VLI_C(0x0B)
+#endif
+
 /* On success, return value >= 0
    On failure, return -1 */
 static inline Py_ssize_t
@@ -379,6 +392,8 @@ lzma_filter_converter(_lzma_state *state, PyObject *spec, void *ptr)
         case LZMA_FILTER_ARM:
         case LZMA_FILTER_ARMTHUMB:
         case LZMA_FILTER_SPARC:
+        case LZMA_FILTER_ARM64:
+        case LZMA_FILTER_RISCV:
             f->options = parse_filter_spec_bcj(state, spec);
             return f->options != NULL;
         default:
@@ -497,7 +512,9 @@ build_filter_spec(const lzma_filter *f)
         case LZMA_FILTER_IA64:
         case LZMA_FILTER_ARM:
         case LZMA_FILTER_ARMTHUMB:
-        case LZMA_FILTER_SPARC: {
+        case LZMA_FILTER_SPARC:
+        case LZMA_FILTER_ARM64:
+        case LZMA_FILTER_RISCV: {
             lzma_options_bcj *options = f->options;
             if (options) {
                 ADD_FIELD(options, start_offset);
@@ -1559,6 +1576,8 @@ lzma_exec(PyObject *module)
     ADD_INT_PREFIX_MACRO(module, FILTER_ARMTHUMB);
     ADD_INT_PREFIX_MACRO(module, FILTER_SPARC);
     ADD_INT_PREFIX_MACRO(module, FILTER_POWERPC);
+    ADD_INT_PREFIX_MACRO(module, FILTER_ARM64);
+    ADD_INT_PREFIX_MACRO(module, FILTER_RISCV);
     ADD_INT_PREFIX_MACRO(module, MF_HC3);
     ADD_INT_PREFIX_MACRO(module, MF_HC4);
     ADD_INT_PREFIX_MACRO(module, MF_BT2);
@@ -1599,6 +1618,27 @@ lzma_exec(PyObject *module)
         return -1;
     }
 
+    if (PyModule_AddStringConstant(
+                module, "LZMA_HEADER_VERSION_STRING",
+                LZMA_VERSION_STRING) < 0) {
+        return -1;
+    }
+    if (PyModule_AddStringConstant(
+                module, "LZMA_VERSION_STRING",
+                lzma_version_string()) < 0) {
+        return -1;
+    }
+    PyObject *uint32_obj = PyLong_FromUnsignedLong(LZMA_VERSION);
+    if (PyModule_AddObject(module, "LZMA_HEADER_VERSION", uint32_obj) < 0) {
+        Py_XDECREF(uint32_obj);
+        return -1;
+    }
+    uint32_obj = PyLong_FromUnsignedLong(lzma_version_number());
+    if (PyModule_AddObject(module, "LZMA_VERSION", uint32_obj) < 0) {
+        Py_XDECREF(uint32_obj);
+        return -1;
+    }
+
     return 0;
 }