diff --git a/core/core/package.json b/core/core/package.json
index aa0d34655..4305623d4 100644
--- a/core/core/package.json
+++ b/core/core/package.json
@@ -48,7 +48,7 @@
     "webpack": "^4.43.0"
   },
   "peerDependencies": {
-    "react": "^16.13.1"
+    "react": ">= 16.8.0"
   },
   "publishConfig": {
     "access": "public"
diff --git a/core/store/package.json b/core/store/package.json
index 27e830c17..4dd2d93ca 100644
--- a/core/store/package.json
+++ b/core/store/package.json
@@ -58,7 +58,7 @@
     "webpack": "^4.41.6"
   },
   "peerDependencies": {
-    "react": "^16.13.1"
+    "react": ">= 16.8.0"
   },
   "publishConfig": {
     "access": "public"
diff --git a/integrations/gatsby-theme-stories/package.json b/integrations/gatsby-theme-stories/package.json
index edbfedac6..b129a474a 100644
--- a/integrations/gatsby-theme-stories/package.json
+++ b/integrations/gatsby-theme-stories/package.json
@@ -56,9 +56,9 @@
     "typescript": "^3.8.3"
   },
   "peerDependencies": {
-    "gatsby": "^2.22.10",
-    "react": "^16.13.1",
-    "react-dom": "^16.13.1"
+    "gatsby": "2.x",
+    "react": ">= 16.8.0",
+    "react-dom": ">= 16.8.0"
   },
   "publishConfig": {
     "access": "public"
diff --git a/integrations/storybook/package.json b/integrations/storybook/package.json
index 23cb13742..4aabb9362 100644
--- a/integrations/storybook/package.json
+++ b/integrations/storybook/package.json
@@ -58,11 +58,11 @@
     "@types/node": "^13.7.0"
   },
   "peerDependencies": {
-    "@storybook/addons": "*",
-    "@storybook/api": "*",
-    "@storybook/client-api": "*",
-    "polished": "*",
-    "react": "*"
+    "@storybook/addons": "5.x 6.x",
+    "@storybook/api": "5.x 6.x",
+    "@storybook/client-api": "5.x 6.x",
+    "polished": "3.x",
+    "react": ">= 16.8.0"
   },
   "publishConfig": {
     "access": "public"
diff --git a/misc/storybook-custom-docs/package.json b/misc/storybook-custom-docs/package.json
index bef075f40..bcee0b4c1 100644
--- a/misc/storybook-custom-docs/package.json
+++ b/misc/storybook-custom-docs/package.json
@@ -48,12 +48,12 @@
     "typescript": "^3.8.3"
   },
   "peerDependencies": {
-    "@storybook/addons": "*",
-    "@storybook/api": "*",
-    "@storybook/client-api": "*",
-    "@storybook/core-events": "*",
-    "react": "^16.13.1",
-    "react-dom": "^16.13.1"
+    "@storybook/addons": "5.x 6.x",
+    "@storybook/api": "5.x 6.x",
+    "@storybook/client-api": "5.x 6.x",
+    "@storybook/core-events": "5.x 6.x",
+    "react": ">= 16.8.0",
+    "react-dom": ">= 16.8.0"
   },
   "publishConfig": {
     "access": "public"
diff --git a/plugins/axe-plugin/package.json b/plugins/axe-plugin/package.json
index 4534af789..c1c785854 100644
--- a/plugins/axe-plugin/package.json
+++ b/plugins/axe-plugin/package.json
@@ -53,8 +53,8 @@
   },
   "peerDependencies": {
     "@component-controls/blocks": "*",
-    "react": "*",
-    "theme-ui": "*"
+    "react": ">= 16.8.0",
+    "theme-ui": "next"
   },
   "publishConfig": {
     "access": "public"
diff --git a/props-info/react-docgen-typescript/package.json b/props-info/react-docgen-typescript/package.json
index a190c23d6..a85d5a390 100644
--- a/props-info/react-docgen-typescript/package.json
+++ b/props-info/react-docgen-typescript/package.json
@@ -44,8 +44,8 @@
     "typescript": "^3.8.3"
   },
   "peerDependencies": {
-    "@component-controls/core": "*",
-    "react": "*"
+    "@component-controls/core": ">= 1.18.1",
+    "react": ">= 16.8.0"
   },
   "jest": {
     "testEnvironment": "node",
diff --git a/props-info/react-docgen/package.json b/props-info/react-docgen/package.json
index a07bd8dd9..b0b5249f1 100644
--- a/props-info/react-docgen/package.json
+++ b/props-info/react-docgen/package.json
@@ -46,8 +46,8 @@
     "typescript": "^3.8.3"
   },
   "peerDependencies": {
-    "@component-controls/core": "*",
-    "react": "*"
+    "@component-controls/core": ">= 1.18.1",
+    "react": ">= 16.8.0"
   },
   "jest": {
     "testEnvironment": "node",
diff --git a/ui/app/package.json b/ui/app/package.json
index 07d645913..8f99754d5 100644
--- a/ui/app/package.json
+++ b/ui/app/package.json
@@ -49,9 +49,9 @@
     "jest": "^24.9.0"
   },
   "peerDependencies": {
-    "react": "^16.13.1",
-    "react-dom": "^16.13.1",
-    "theme-ui": "*"
+    "react": ">= 16.8.0",
+    "react-dom": ">= 16.8.0",
+    "theme-ui": "next"
   },
   "publishConfig": {
     "access": "public"
diff --git a/ui/blocks/package.json b/ui/blocks/package.json
index 9d444bc90..d2d55d59f 100644
--- a/ui/blocks/package.json
+++ b/ui/blocks/package.json
@@ -64,11 +64,11 @@
     "jest": "^24.9.0"
   },
   "peerDependencies": {
-    "@primer/octicons-react": "*",
-    "react": "^16.13.1",
-    "react-dom": "^16.13.1",
-    "react-table": "*",
-    "theme-ui": "*"
+    "@primer/octicons-react": "10.x",
+    "react": ">= 16.8.0",
+    "react-dom": ">= 16.8.0",
+    "react-table": "7.x",
+    "theme-ui": "next"
   },
   "publishConfig": {
     "access": "public"
diff --git a/ui/components/package.json b/ui/components/package.json
index da6e692b9..295fe6f6f 100644
--- a/ui/components/package.json
+++ b/ui/components/package.json
@@ -60,10 +60,10 @@
     "jest": "^24.9.0"
   },
   "peerDependencies": {
-    "@theme-ui/css": "*",
-    "react": "^16.13.1",
-    "react-dom": "^16.13.1",
-    "theme-ui": "*"
+    "@theme-ui/css": "next",
+    "react": ">= 16.8.0",
+    "react-dom": ">= 16.8.0",
+    "theme-ui": "next"
   },
   "publishConfig": {
     "access": "public"
diff --git a/ui/editors/package.json b/ui/editors/package.json
index 827260715..c97b32248 100644
--- a/ui/editors/package.json
+++ b/ui/editors/package.json
@@ -53,9 +53,9 @@
     "jest": "^24.9.0"
   },
   "peerDependencies": {
-    "@primer/octicons-react": "*",
-    "react": "^16.13.1",
-    "react-dom": "^16.13.1"
+    "@primer/octicons-react": "10.x",
+    "react": ">= 16.8.0",
+    "react-dom": ">= 16.8.0"
   },
   "publishConfig": {
     "access": "public"
diff --git a/ui/pages/package.json b/ui/pages/package.json
index 6df74daeb..b7b4e3622 100644
--- a/ui/pages/package.json
+++ b/ui/pages/package.json
@@ -42,7 +42,7 @@
     "jest": "^24.9.0"
   },
   "peerDependencies": {
-    "react": "*"
+    "react": ">= 16.8.0"
   },
   "publishConfig": {
     "access": "public"