diff --git a/block/curl.c b/block/curl.c
index cba4c4cac7..0b125095e3 100644
--- a/block/curl.c
+++ b/block/curl.c
@@ -37,8 +37,15 @@
 
 // #define DEBUG_VERBOSE
 
+/* CURL 7.85.0 switches to a string based API for specifying
+ * the desired protocols.
+ */
+#if LIBCURL_VERSION_NUM >= 0x075500
+#define PROTOCOLS "HTTP,HTTPS,FTP,FTPS"
+#else
 #define PROTOCOLS (CURLPROTO_HTTP | CURLPROTO_HTTPS | \
                    CURLPROTO_FTP | CURLPROTO_FTPS)
+#endif
 
 #define CURL_NUM_STATES 8
 #define CURL_NUM_ACB    8
@@ -509,9 +516,18 @@ static int curl_init_state(BDRVCURLState *s, CURLState *state)
          * obscure protocols.  For example, do not allow POP3/SMTP/IMAP see
          * CVE-2013-0249.
          *
-         * Restricting protocols is only supported from 7.19.4 upwards.
+         * Restricting protocols is only supported from 7.19.4 upwards. Note:
+         * version 7.85.0 deprecates CURLOPT_*PROTOCOLS in favour of a string
+         * based CURLOPT_*PROTOCOLS_STR API.
          */
-#if LIBCURL_VERSION_NUM >= 0x071304
+#if LIBCURL_VERSION_NUM >= 0x075500
+        if (curl_easy_setopt(state->curl,
+                             CURLOPT_PROTOCOLS_STR, PROTOCOLS) ||
+            curl_easy_setopt(state->curl,
+                             CURLOPT_REDIR_PROTOCOLS_STR, PROTOCOLS)) {
+            goto err;
+        }
+#elif LIBCURL_VERSION_NUM >= 0x071304
         if (curl_easy_setopt(state->curl, CURLOPT_PROTOCOLS, PROTOCOLS) ||
             curl_easy_setopt(state->curl, CURLOPT_REDIR_PROTOCOLS, PROTOCOLS)) {
             goto err;
@@ -669,7 +685,12 @@ static int curl_open(BlockDriverState *bs, QDict *options, int flags,
     const char *file;
     const char *cookie;
     const char *cookie_secret;
-    double d;
+    /* CURL >= 7.55.0 uses curl_off_t for content length instead of a double */
+#if LIBCURL_VERSION_NUM >= 0x073700
+    curl_off_t cl;
+#else
+    double cl;
+#endif
     const char *secretid;
     const char *protocol_delimiter;
     int ret;
@@ -796,27 +817,36 @@ static int curl_open(BlockDriverState *bs, QDict *options, int flags,
     }
     if (curl_easy_perform(state->curl))
         goto out;
-    if (curl_easy_getinfo(state->curl, CURLINFO_CONTENT_LENGTH_DOWNLOAD, &d)) {
+    /* CURL 7.55.0 deprecates CURLINFO_CONTENT_LENGTH_DOWNLOAD in favour of
+     * the *_T version which returns a more sensible type for content length.
+     */
+#if LIBCURL_VERSION_NUM >= 0x073700
+    if (curl_easy_getinfo(state->curl, CURLINFO_CONTENT_LENGTH_DOWNLOAD_T, &cl)) {
         goto out;
     }
+#else
+    if (curl_easy_getinfo(state->curl, CURLINFO_CONTENT_LENGTH_DOWNLOAD, &cl)) {
+        goto out;
+    }
+#endif
     /* Prior CURL 7.19.4 return value of 0 could mean that the file size is not
      * know or the size is zero. From 7.19.4 CURL returns -1 if size is not
      * known and zero if it is really zero-length file. */
 #if LIBCURL_VERSION_NUM >= 0x071304
-    if (d < 0) {
+    if (cl < 0) {
         pstrcpy(state->errmsg, CURL_ERROR_SIZE,
                 "Server didn't report file size.");
         goto out;
     }
 #else
-    if (d <= 0) {
+    if (cl <= 0) {
         pstrcpy(state->errmsg, CURL_ERROR_SIZE,
                 "Unknown file size or zero-length file.");
         goto out;
     }
 #endif
 
-    s->len = d;
+    s->len = cl;
 
     if ((!strncasecmp(s->url, "http://", strlen("http://"))
         || !strncasecmp(s->url, "https://", strlen("https://")))