diff --git a/deps/nghttp2/lib/CMakeLists.txt b/deps/nghttp2/lib/CMakeLists.txt
index 17e422b22db790..c27ee99bb7fa46 100644
--- a/deps/nghttp2/lib/CMakeLists.txt
+++ b/deps/nghttp2/lib/CMakeLists.txt
@@ -38,16 +38,23 @@ if(WIN32)
 endif()
 
 # Public shared library
-add_library(nghttp2 SHARED ${NGHTTP2_SOURCES} ${NGHTTP2_RES})
-set_target_properties(nghttp2 PROPERTIES
-  COMPILE_FLAGS "${WARNCFLAGS}"
-  VERSION ${LT_VERSION} SOVERSION ${LT_SOVERSION}
-  C_VISIBILITY_PRESET hidden
-)
-target_include_directories(nghttp2 INTERFACE
+if(ENABLE_SHARED_LIB)
+  add_library(nghttp2 SHARED ${NGHTTP2_SOURCES} ${NGHTTP2_RES})
+  set_target_properties(nghttp2 PROPERTIES
+    COMPILE_FLAGS "${WARNCFLAGS}"
+    VERSION ${LT_VERSION} SOVERSION ${LT_SOVERSION}
+    C_VISIBILITY_PRESET hidden
+  )
+  target_include_directories(nghttp2 INTERFACE
     "${CMAKE_CURRENT_BINARY_DIR}/includes"
     "${CMAKE_CURRENT_SOURCE_DIR}/includes"
-    )
+  )
+
+  install(TARGETS nghttp2
+    ARCHIVE DESTINATION "${CMAKE_INSTALL_LIBDIR}"
+    LIBRARY DESTINATION "${CMAKE_INSTALL_LIBDIR}"
+    RUNTIME DESTINATION "${CMAKE_INSTALL_BINDIR}")
+endif()
 
 if(HAVE_CUNIT OR ENABLE_STATIC_LIB)
   # Static library (for unittests because of symbol visibility)
@@ -64,8 +71,6 @@ if(HAVE_CUNIT OR ENABLE_STATIC_LIB)
   endif()
 endif()
 
-install(TARGETS nghttp2
-  DESTINATION "${CMAKE_INSTALL_LIBDIR}")
 
 install(FILES "${CMAKE_CURRENT_BINARY_DIR}/libnghttp2.pc"
   DESTINATION "${CMAKE_INSTALL_LIBDIR}/pkgconfig")
diff --git a/deps/nghttp2/lib/includes/nghttp2/nghttp2.h b/deps/nghttp2/lib/includes/nghttp2/nghttp2.h
index e7198b3d27314d..925a4cbcaf6d6a 100644
--- a/deps/nghttp2/lib/includes/nghttp2/nghttp2.h
+++ b/deps/nghttp2/lib/includes/nghttp2/nghttp2.h
@@ -31,6 +31,11 @@
 #  define WIN32
 #endif
 
+/* Compatibility for non-Clang compilers */
+#ifndef __has_declspec_attribute
+#  define __has_declspec_attribute(x) 0
+#endif
+
 #ifdef __cplusplus
 extern "C" {
 #endif
@@ -51,7 +56,8 @@ extern "C" {
 
 #ifdef NGHTTP2_STATICLIB
 #  define NGHTTP2_EXTERN
-#elif defined(WIN32)
+#elif defined(WIN32) || (__has_declspec_attribute(dllexport) &&                \
+                         __has_declspec_attribute(dllimport))
 #  ifdef BUILDING_NGHTTP2
 #    define NGHTTP2_EXTERN __declspec(dllexport)
 #  else /* !BUILDING_NGHTTP2 */
diff --git a/deps/nghttp2/lib/includes/nghttp2/nghttp2ver.h b/deps/nghttp2/lib/includes/nghttp2/nghttp2ver.h
index 420adbd53dddce..2384f5278773cb 100644
--- a/deps/nghttp2/lib/includes/nghttp2/nghttp2ver.h
+++ b/deps/nghttp2/lib/includes/nghttp2/nghttp2ver.h
@@ -29,7 +29,7 @@
  * @macro
  * Version number of the nghttp2 library release
  */
-#define NGHTTP2_VERSION "1.34.0"
+#define NGHTTP2_VERSION "1.37.0"
 
 /**
  * @macro
@@ -37,6 +37,6 @@
  * release. This is a 24 bit number with 8 bits for major number, 8 bits
  * for minor and 8 bits for patch. Version 1.2.3 becomes 0x010203.
  */
-#define NGHTTP2_VERSION_NUM 0x012200
+#define NGHTTP2_VERSION_NUM 0x012500
 
 #endif /* NGHTTP2VER_H */
diff --git a/deps/nghttp2/lib/nghttp2_hd.c b/deps/nghttp2/lib/nghttp2_hd.c
index a61f0d47a6f79d..11ca3345f3c6b3 100644
--- a/deps/nghttp2/lib/nghttp2_hd.c
+++ b/deps/nghttp2/lib/nghttp2_hd.c
@@ -1390,7 +1390,7 @@ static int deflate_nv(nghttp2_hd_deflater *deflater, nghttp2_bufs *bufs,
   if (indexing_mode == NGHTTP2_HD_WITH_INDEXING) {
     nghttp2_hd_nv hd_nv;
 
-    if (idx != -1 && idx < (ssize_t)NGHTTP2_STATIC_TABLE_LENGTH) {
+    if (idx != -1) {
       hd_nv.name = nghttp2_hd_table_get(&deflater->ctx, (size_t)idx).name;
       nghttp2_rcbuf_incref(hd_nv.name);
     } else {
diff --git a/deps/nghttp2/lib/nghttp2_session.h b/deps/nghttp2/lib/nghttp2_session.h
index 40a8865a04b12f..bd7a5b35817599 100644
--- a/deps/nghttp2/lib/nghttp2_session.h
+++ b/deps/nghttp2/lib/nghttp2_session.h
@@ -209,9 +209,6 @@ struct nghttp2_session {
   nghttp2_session_callbacks callbacks;
   /* Memory allocator */
   nghttp2_mem mem;
-  /* Base value when we schedule next DATA frame write.  This is
-     updated when one frame was written. */
-  uint64_t last_cycle;
   void *user_data;
   /* Points to the latest incoming closed stream.  NULL if there is no
      closed stream.  Only used when session is initialized as
diff --git a/deps/nghttp2/lib/nghttp2_stream.c b/deps/nghttp2/lib/nghttp2_stream.c
index eccd3174ef7bda..dc3a6b11ccbf75 100644
--- a/deps/nghttp2/lib/nghttp2_stream.c
+++ b/deps/nghttp2/lib/nghttp2_stream.c
@@ -30,6 +30,7 @@
 #include "nghttp2_session.h"
 #include "nghttp2_helper.h"
 #include "nghttp2_debug.h"
+#include "nghttp2_frame.h"
 
 /* Maximum distance between any two stream's cycle in the same
    prirority queue.  Imagine stream A's cycle is A, and stream B's
@@ -40,7 +41,8 @@
    words, B is really greater than or equal to A.  Otherwise, A is a
    result of overflow, and it is actually A > B if we consider that
    fact. */
-#define NGHTTP2_MAX_CYCLE_DISTANCE (16384 * 256 + 255)
+#define NGHTTP2_MAX_CYCLE_DISTANCE                                             \
+  ((uint64_t)NGHTTP2_MAX_FRAME_SIZE_MAX * 256 + 255)
 
 static int stream_less(const void *lhsx, const void *rhsx) {
   const nghttp2_stream *lhs, *rhs;
@@ -52,11 +54,7 @@ static int stream_less(const void *lhsx, const void *rhsx) {
     return lhs->seq < rhs->seq;
   }
 
-  if (lhs->cycle < rhs->cycle) {
-    return rhs->cycle - lhs->cycle <= NGHTTP2_MAX_CYCLE_DISTANCE;
-  }
-
-  return lhs->cycle - rhs->cycle > NGHTTP2_MAX_CYCLE_DISTANCE;
+  return rhs->cycle - lhs->cycle <= NGHTTP2_MAX_CYCLE_DISTANCE;
 }
 
 void nghttp2_stream_init(nghttp2_stream *stream, int32_t stream_id,
@@ -135,14 +133,14 @@ static int stream_subtree_active(nghttp2_stream *stream) {
 /*
  * Returns next cycle for |stream|.
  */
-static void stream_next_cycle(nghttp2_stream *stream, uint32_t last_cycle) {
-  uint32_t penalty;
+static void stream_next_cycle(nghttp2_stream *stream, uint64_t last_cycle) {
+  uint64_t penalty;
 
-  penalty = (uint32_t)stream->last_writelen * NGHTTP2_MAX_WEIGHT +
+  penalty = (uint64_t)stream->last_writelen * NGHTTP2_MAX_WEIGHT +
             stream->pending_penalty;
 
   stream->cycle = last_cycle + penalty / (uint32_t)stream->weight;
-  stream->pending_penalty = penalty % (uint32_t)stream->weight;
+  stream->pending_penalty = (uint32_t)(penalty % (uint32_t)stream->weight);
 }
 
 static int stream_obq_push(nghttp2_stream *dep_stream, nghttp2_stream *stream) {
@@ -153,7 +151,7 @@ static int stream_obq_push(nghttp2_stream *dep_stream, nghttp2_stream *stream) {
     stream_next_cycle(stream, dep_stream->descendant_last_cycle);
     stream->seq = dep_stream->descendant_next_seq++;
 
-    DEBUGF("stream: stream=%d obq push cycle=%d\n", stream->stream_id,
+    DEBUGF("stream: stream=%d obq push cycle=%lu\n", stream->stream_id,
            stream->cycle);
 
     DEBUGF("stream: push stream %d to stream %d\n", stream->stream_id,
@@ -239,7 +237,7 @@ void nghttp2_stream_reschedule(nghttp2_stream *stream) {
 
     nghttp2_pq_push(&dep_stream->obq, &stream->pq_entry);
 
-    DEBUGF("stream: stream=%d obq resched cycle=%d\n", stream->stream_id,
+    DEBUGF("stream: stream=%d obq resched cycle=%lu\n", stream->stream_id,
            stream->cycle);
 
     dep_stream->last_writelen = stream->last_writelen;
@@ -248,9 +246,9 @@ void nghttp2_stream_reschedule(nghttp2_stream *stream) {
 
 void nghttp2_stream_change_weight(nghttp2_stream *stream, int32_t weight) {
   nghttp2_stream *dep_stream;
-  uint32_t last_cycle;
+  uint64_t last_cycle;
   int32_t old_weight;
-  uint32_t wlen_penalty;
+  uint64_t wlen_penalty;
 
   if (stream->weight == weight) {
     return;
@@ -273,7 +271,7 @@ void nghttp2_stream_change_weight(nghttp2_stream *stream, int32_t weight) {
 
   nghttp2_pq_remove(&dep_stream->obq, &stream->pq_entry);
 
-  wlen_penalty = (uint32_t)stream->last_writelen * NGHTTP2_MAX_WEIGHT;
+  wlen_penalty = (uint64_t)stream->last_writelen * NGHTTP2_MAX_WEIGHT;
 
   /* Compute old stream->pending_penalty we used to calculate
      stream->cycle */
@@ -289,9 +287,8 @@ void nghttp2_stream_change_weight(nghttp2_stream *stream, int32_t weight) {
      place */
   stream_next_cycle(stream, last_cycle);
 
-  if (stream->cycle < dep_stream->descendant_last_cycle &&
-      (dep_stream->descendant_last_cycle - stream->cycle) <=
-          NGHTTP2_MAX_CYCLE_DISTANCE) {
+  if (dep_stream->descendant_last_cycle - stream->cycle <=
+      NGHTTP2_MAX_CYCLE_DISTANCE) {
     stream->cycle = dep_stream->descendant_last_cycle;
   }
 
@@ -299,7 +296,7 @@ void nghttp2_stream_change_weight(nghttp2_stream *stream, int32_t weight) {
 
   nghttp2_pq_push(&dep_stream->obq, &stream->pq_entry);
 
-  DEBUGF("stream: stream=%d obq resched cycle=%d\n", stream->stream_id,
+  DEBUGF("stream: stream=%d obq resched cycle=%lu\n", stream->stream_id,
          stream->cycle);
 }
 
diff --git a/deps/nghttp2/lib/nghttp2_stream.h b/deps/nghttp2/lib/nghttp2_stream.h
index fb8dc14d67be6d..a1b807d295c05c 100644
--- a/deps/nghttp2/lib/nghttp2_stream.h
+++ b/deps/nghttp2/lib/nghttp2_stream.h
@@ -148,9 +148,9 @@ struct nghttp2_stream {
   /* Received body so far */
   int64_t recv_content_length;
   /* Base last_cycle for direct descendent streams. */
-  uint32_t descendant_last_cycle;
+  uint64_t descendant_last_cycle;
   /* Next scheduled time to sent item */
-  uint32_t cycle;
+  uint64_t cycle;
   /* Next seq used for direct descendant streams */
   uint64_t descendant_next_seq;
   /* Secondary key for prioritization to break a tie for cycle.  This