diff --git a/newsfragments/941.feature.rst b/newsfragments/941.feature.rst
new file mode 100644
index 0000000000..9c0f4764fe
--- /dev/null
+++ b/newsfragments/941.feature.rst
@@ -0,0 +1 @@
+Raise `SolidityError` exceptions that contain the revert reason when a `call` fails.
diff --git a/tests/core/utilities/test_method_formatters.py b/tests/core/utilities/test_method_formatters.py
new file mode 100644
index 0000000000..2bd50cb279
--- /dev/null
+++ b/tests/core/utilities/test_method_formatters.py
@@ -0,0 +1,65 @@
+import pytest
+
+from web3._utils.method_formatters import (
+    get_error_formatters,
+    get_revert_reason,
+)
+from web3._utils.rpc_abi import (
+    RPC,
+)
+from web3.exceptions import (
+    SolidityError,
+)
+from web3.types import (
+    RPCResponse,
+)
+
+REVERT_WITH_MSG = RPCResponse({
+    'jsonrpc': '2.0',
+    'error': {
+        'code': -32015,
+        'message': 'VM execution error.',
+        'data': (
+            'Reverted '
+            '0x08c379a'
+            '00000000000000000000000000000000000000000000000000000000000000020'
+            '0000000000000000000000000000000000000000000000000000000000000016'
+            '6e6f7420616c6c6f77656420746f206d6f6e69746f7200000000000000000000'
+        ),
+    },
+    'id': 2987,
+})
+
+REVERT_WITHOUT_MSG = RPCResponse({
+    'jsonrpc': '2.0',
+    'error': {
+        'code': -32015,
+        'message': 'VM execution error.',
+        'data': 'Reverted 0x',
+    },
+    'id': 2987,
+})
+
+OTHER_ERROR = RPCResponse({
+    "jsonrpc": "2.0",
+    "error": {
+        "code": -32601,
+        "message": "Method not found",
+    },
+    "id": 1,
+})
+
+
+def test_get_revert_reason() -> None:
+    assert get_revert_reason(REVERT_WITH_MSG) == 'not allowed to monitor'
+    assert get_revert_reason(REVERT_WITHOUT_MSG) == ''
+    assert get_revert_reason(OTHER_ERROR) is None
+
+
+def test_get_error_formatters() -> None:
+    formatters = get_error_formatters(RPC.eth_call)
+    with pytest.raises(SolidityError, match='not allowed to monitor'):
+        formatters(REVERT_WITH_MSG)
+    with pytest.raises(SolidityError):
+        formatters(REVERT_WITHOUT_MSG)
+    assert formatters(OTHER_ERROR) == OTHER_ERROR
diff --git a/web3/_utils/method_formatters.py b/web3/_utils/method_formatters.py
index 4ad32eea9f..53b18cc737 100644
--- a/web3/_utils/method_formatters.py
+++ b/web3/_utils/method_formatters.py
@@ -67,8 +67,12 @@
 from web3.datastructures import (
     AttributeDict,
 )
+from web3.exceptions import (
+    SolidityError,
+)
 from web3.types import (
     RPCEndpoint,
+    RPCResponse,
     TReturn,
 )
 
@@ -431,7 +435,6 @@ def apply_list_to_array_formatter(formatter: Any) -> Callable[..., Any]:
     RPC.net_peerCount: to_integer_if_hex,
 }
 
-
 ATTRDICT_FORMATTER = {
     '*': apply_formatter_if(is_dict and not_attrdict, AttributeDict.recursive)
 }
@@ -452,6 +455,54 @@ def apply_list_to_array_formatter(formatter: Any) -> Callable[..., Any]:
 ABI_REQUEST_FORMATTERS = abi_request_formatters(STANDARD_NORMALIZERS, RPC_ABIS)
 
 
+def get_revert_reason(response: RPCResponse) -> str:
+    """
+    Parse revert reason from response, return None if no revert happened.
+
+    If a revert happened, but no message has been given, return an empty string.
+
+    Reverts contain a `data` attribute with the following layout:
+        "Reverted "
+        Function selector for Error(string): 08c379a (4 bytes)
+        Data offset: 32 (32 bytes)
+        String length (32 bytes)
+        Reason strong (padded, use string length from above to get meaningful part)
+
+    See also https://solidity.readthedocs.io/en/v0.6.3/control-structures.html#revert
+    """
+    assert 'error' in response
+    if not isinstance(response['error'], dict):
+        return None
+
+    data = response['error'].get('data', '')
+
+    if data == 'Reverted 0x':
+        return ''
+
+    # "Reverted", function selector and offset are always the same for revert errors
+    prefix = 'Reverted 0x08c379a00000000000000000000000000000000000000000000000000000000000000020'
+    if not data.startswith(prefix):
+        return None
+
+    reason_length = int(data[len(prefix):len(prefix) + 64], 16)
+    reason = data[len(prefix) + 64:len(prefix) + 64 + reason_length * 2]
+    return bytes.fromhex(reason).decode('utf8')
+
+
+def raise_solidity_error_on_revert(response: RPCResponse) -> RPCResponse:
+    revert_reason = get_revert_reason(response)
+    if revert_reason is None:
+        return response
+    if revert_reason == '':
+        raise SolidityError()
+    raise SolidityError(revert_reason)
+
+
+ERROR_FORMATTERS: Dict[RPCEndpoint, Callable[..., Any]] = {
+    RPC.eth_call: raise_solidity_error_on_revert,
+}
+
+
 @to_tuple
 def combine_formatters(
     formatter_maps: Collection[Dict[RPCEndpoint, Callable[..., TReturn]]], method_name: RPCEndpoint
@@ -487,10 +538,9 @@ def get_result_formatters(
 
 def get_error_formatters(
     method_name: Union[RPCEndpoint, Callable[..., RPCEndpoint]]
-) -> Dict[str, Callable[..., Any]]:
+) -> Callable[..., Any]:
     #  Note error formatters work on the full response dict
-    # TODO - test this function
-    error_formatter_maps = ()
+    error_formatter_maps = (ERROR_FORMATTERS, )
     formatters = combine_formatters(error_formatter_maps, method_name)
 
     return compose(*formatters)
diff --git a/web3/exceptions.py b/web3/exceptions.py
index 2241d887e3..b363206fbe 100644
--- a/web3/exceptions.py
+++ b/web3/exceptions.py
@@ -169,3 +169,11 @@ class InvalidEventABI(ValueError):
     Raised when the event ABI is invalid.
     """
     pass
+
+
+class SolidityError(ValueError):
+    # Inherits from ValueError for backwards compatibility
+    """
+    Raised on a solidity require/revert
+    """
+    pass
diff --git a/web3/manager.py b/web3/manager.py
index 54b3e94a73..89909482b0 100644
--- a/web3/manager.py
+++ b/web3/manager.py
@@ -149,7 +149,7 @@ def request_blocking(
         response = self._make_request(method, params)
 
         if "error" in response:
-            apply_error_formatters(error_formatters, response)
+            response = apply_error_formatters(error_formatters, response)
             raise ValueError(response["error"])
 
         return response['result']
diff --git a/web3/types.py b/web3/types.py
index 66e042a38f..c218c01e83 100644
--- a/web3/types.py
+++ b/web3/types.py
@@ -109,6 +109,7 @@ class EventData(TypedDict):
 class RPCError(TypedDict):
     code: int
     message: str
+    data: Optional[str]
 
 
 class RPCResponse(TypedDict, total=False):