diff --git a/autograd/numpy/numpy_boxes.py b/autograd/numpy/numpy_boxes.py
index b9c73963..a5fab2a7 100644
--- a/autograd/numpy/numpy_boxes.py
+++ b/autograd/numpy/numpy_boxes.py
@@ -4,6 +4,7 @@
 
 from autograd.builtins import SequenceBox
 from autograd.extend import Box, primitive
+from autograd.tracer import trace_primitives_map
 
 from . import numpy_wrapper as anp
 
@@ -18,16 +19,40 @@ class ArrayBox(Box):
     def __getitem__(A, idx):
         return A[idx]
 
-    # Constants w.r.t float data just pass though
-    shape = property(lambda self: self._value.shape)
-    ndim = property(lambda self: self._value.ndim)
-    size = property(lambda self: self._value.size)
-    dtype = property(lambda self: self._value.dtype)
+    # Basic array attributes just pass through
+    # Single wrapped scalars are presented as 0-dim, 1-size arrays.
+    shape = property(lambda self: anp.shape(self._value))
+    ndim = property(lambda self: anp.ndim(self._value))
+    size = property(lambda self: anp.size(self._value))
+    dtype = property(lambda self: anp.result_type(self._value))
+
     T = property(lambda self: anp.transpose(self))
 
     def __array_namespace__(self, *, api_version: Union[str, None] = None):
         return anp
 
+    # Calls to wrapped ufuncs first forward further handling to the ufunc
+    # dispatching mechanism, which allows any other operands to also try
+    # handling the ufunc call. See also tracer.primitive.
+    #
+    # In addition, implementing __array_ufunc__ allows ufunc calls to propagate
+    # through non-differentiable array-like objects (e.g. xarray.DataArray) into
+    # ArrayBoxes which might be contained within, upon which __array_ufunc__
+    # below would call autograd's wrapper for the ufunc. For example, given a
+    # DataArray `a` containing an ArrayBox, this lets us write `np.abs(a)`
+    # instead of requiring the xarray-specific `xr.apply_func(np.abs, a)`.
+    def __array_ufunc__(self, ufunc, method, *inputs, **kwargs):
+        if method != "__call__":
+            return NotImplemented
+        if "out" in kwargs:
+            return NotImplemented
+        if ufunc_wrapper := trace_primitives_map.get(ufunc):
+            try:
+                return ufunc_wrapper(*inputs, called_by_autograd_dispatcher=True, **kwargs)
+            except NotImplementedError:
+                return NotImplemented
+        return NotImplemented
+
     def __len__(self):
         return len(self._value)
 
diff --git a/autograd/numpy/numpy_wrapper.py b/autograd/numpy/numpy_wrapper.py
index ab97f214..1f7fe49c 100644
--- a/autograd/numpy/numpy_wrapper.py
+++ b/autograd/numpy/numpy_wrapper.py
@@ -25,15 +25,29 @@ class IntdtypeSubclass(cls):
 def wrap_namespace(old, new):
     unchanged_types = {float, int, type(None), type}
     int_types = {_np.int8, _np.int16, _np.int32, _np.int64, _np.integer}
+    obj_to_wrapped = []
     for name, obj in old.items():
-        if obj in notrace_functions:
-            new[name] = notrace_primitive(obj)
-        elif callable(obj) and type(obj) is not type:
-            new[name] = primitive(obj)
-        elif type(obj) is type and obj in int_types:
-            new[name] = wrap_intdtype(obj)
-        elif type(obj) in unchanged_types:
-            new[name] = obj
+        # Map multiple names of the same object (e.g. conj/conjugate)
+        # to the same wrapped object
+        for mapped_obj, wrapped in obj_to_wrapped:
+            if mapped_obj is obj:
+                new[name] = wrapped
+                break
+        else:
+            if obj in notrace_functions:
+                wrapped = notrace_primitive(obj)
+                new[name] = wrapped
+                obj_to_wrapped.append((obj, wrapped))
+            elif callable(obj) and type(obj) is not type:
+                wrapped = primitive(obj)
+                new[name] = wrapped
+                obj_to_wrapped.append((obj, wrapped))
+            elif type(obj) is type and obj in int_types:
+                wrapped = wrap_intdtype(obj)
+                new[name] = wrapped
+                obj_to_wrapped.append((obj, wrapped))
+            elif type(obj) in unchanged_types:
+                new[name] = obj
 
 
 wrap_namespace(_np.__dict__, globals())
diff --git a/autograd/tracer.py b/autograd/tracer.py
index 30fa72a6..a42d66bc 100644
--- a/autograd/tracer.py
+++ b/autograd/tracer.py
@@ -2,6 +2,10 @@
 from collections import defaultdict
 from contextlib import contextmanager
 
+import numpy as np
+
+import autograd
+
 from .util import subvals, toposort
 from .wrap_util import wraps
 
@@ -33,28 +37,61 @@ def new_root(cls, *args, **kwargs):
         return root
 
 
+trace_primitives_map = {}
+
+
 def primitive(f_raw):
     """
     Wraps a function so that its gradient can be specified and its invocation
     can be recorded. For examples, see the docs."""
 
     @wraps(f_raw)
-    def f_wrapped(*args, **kwargs):
+    def f_wrapped(*args, called_by_autograd_dispatcher=False, **kwargs):
         boxed_args, trace, node_constructor = find_top_boxed_args(args)
         if boxed_args:
+            # If we are a wrapper around a ufunc, first forward further handling to
+            # the ufunc dispatching mechanism (if we aren't already running inside it)
+            # by calling the ufunc. This allows other operands to also try to handle
+            # the call (it's still possible our handling attempt below will get the
+            # first shot; the handlers order is determined by the dispatch mechanism).
+            #
+            # For example, consider multiplying an ndarray wrapped inside an ArrayBox
+            # by an xarray.DataArray. The handling below will fail: The ndarray will
+            # be unboxed and multiplied by the DataArray resulting in a DataArray,
+            # for which `new_box` will raise an exception. In contrast, the DataArray's
+            # handling of the call might succeed: it might contain an ndarray, either
+            # plain or boxed in an ArrayBox, in which case it will be multiplied by
+            # the other ArrayBox yielding a new ArrayBox, which will be stored in a new
+            # DataArray.
+            if (
+                isinstance(f_raw, np.ufunc)
+                and not called_by_autograd_dispatcher
+                and any(isinstance(arg, autograd.numpy.numpy_boxes.ArrayBox) for arg in args)
+            ):
+                return f_raw(*args, **kwargs)
+
             argvals = subvals(args, [(argnum, box._value) for argnum, box in boxed_args])
             if f_wrapped in notrace_primitives[node_constructor]:
-                return f_wrapped(*argvals, **kwargs)
+                return f_wrapped(
+                    *argvals, called_by_autograd_dispatcher=called_by_autograd_dispatcher, **kwargs
+                )
             parents = tuple(box._node for _, box in boxed_args)
             argnums = tuple(argnum for argnum, _ in boxed_args)
-            ans = f_wrapped(*argvals, **kwargs)
+            ans = f_wrapped(*argvals, called_by_autograd_dispatcher=called_by_autograd_dispatcher, **kwargs)
             node = node_constructor(ans, f_wrapped, argvals, kwargs, argnums, parents)
-            return new_box(ans, trace, node)
+            try:
+                box = new_box(ans, trace, node)
+                return box
+            except:
+                if called_by_autograd_dispatcher:
+                    raise NotImplementedError
+                raise
         else:
             return f_raw(*args, **kwargs)
 
     f_wrapped.fun = f_raw
     f_wrapped._is_autograd_primitive = True
+    trace_primitives_map[f_raw] = f_wrapped
     return f_wrapped