diff --git a/pandas/_libs/tslib.pyx b/pandas/_libs/tslib.pyx
index 01e500a80dcc4..dc06a30004d19 100644
--- a/pandas/_libs/tslib.pyx
+++ b/pandas/_libs/tslib.pyx
@@ -344,14 +344,13 @@ def array_with_unit_to_datetime(ndarray values, object unit,
         # try a quick conversion to i8
         # if we have nulls that are not type-compat
         # then need to iterate
-        try:
+        if values.dtype.kind == "i":
+            # Note: this condition makes the casting="same_kind" redundant
             iresult = values.astype('i8', casting='same_kind', copy=False)
             mask = iresult == NPY_NAT
             iresult[mask] = 0
             fvalues = iresult.astype('f8') * m
             need_to_iterate = False
-        except:
-            pass
 
         # check the bounds
         if not need_to_iterate:
@@ -406,7 +405,7 @@ def array_with_unit_to_datetime(ndarray values, object unit,
                         elif is_ignore:
                             raise AssertionError
                         iresult[i] = NPY_NAT
-                    except:
+                    except OverflowError:
                         if is_raise:
                             raise OutOfBoundsDatetime(
                                 "cannot convert input {val} with the unit "
@@ -447,7 +446,7 @@ def array_with_unit_to_datetime(ndarray values, object unit,
             else:
                 try:
                     oresult[i] = Timestamp(cast_from_unit(val, unit))
-                except:
+                except OverflowError:
                     oresult[i] = val
 
         elif isinstance(val, str):
@@ -574,7 +573,7 @@ cpdef array_to_datetime(ndarray[object] values, str errors='raise',
                         # datetimes/strings, then we must coerce)
                         try:
                             iresult[i] = cast_from_unit(val, 'ns')
-                        except:
+                        except OverflowError:
                             iresult[i] = NPY_NAT
 
                 elif isinstance(val, str):
diff --git a/pandas/_libs/tslibs/parsing.pyx b/pandas/_libs/tslibs/parsing.pyx
index eb99f090e8565..3da3d1e4b1b41 100644
--- a/pandas/_libs/tslibs/parsing.pyx
+++ b/pandas/_libs/tslibs/parsing.pyx
@@ -587,15 +587,11 @@ def try_parse_dates(object[:] values, parser=None,
     else:
         parse_date = parser
 
-        try:
-            for i in range(n):
-                if values[i] == '':
-                    result[i] = np.nan
-                else:
-                    result[i] = parse_date(values[i])
-        except Exception:
-            # raise if passed parser and it failed
-            raise
+        for i in range(n):
+            if values[i] == '':
+                result[i] = np.nan
+            else:
+                result[i] = parse_date(values[i])
 
     return result.base  # .base to access underlying ndarray
 
@@ -814,7 +810,7 @@ def _guess_datetime_format(dt_str, dayfirst=False, dt_str_parse=du_parse,
     if dt_str_parse is None or dt_str_split is None:
         return None
 
-    if not isinstance(dt_str, (str, unicode)):
+    if not isinstance(dt_str, str):
         return None
 
     day_attribute_and_format = (('day',), '%d', 2)
@@ -840,19 +836,16 @@ def _guess_datetime_format(dt_str, dayfirst=False, dt_str_parse=du_parse,
 
     try:
         parsed_datetime = dt_str_parse(dt_str, dayfirst=dayfirst)
-    except:
+    except (ValueError, OverflowError):
         # In case the datetime can't be parsed, its format cannot be guessed
         return None
 
     if parsed_datetime is None:
         return None
 
-    try:
-        tokens = dt_str_split(dt_str)
-    except:
-        # In case the datetime string can't be split, its format cannot
-        # be guessed
-        return None
+    # the default dt_str_split from dateutil will never raise here; we assume
+    #  that any user-provided function will not either.
+    tokens = dt_str_split(dt_str)
 
     format_guess = [None] * len(tokens)
     found_attrs = set()