diff --git a/NEWS.md b/NEWS.md
index 751442932..b642f2cb2 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -2,20 +2,22 @@
 
 - Interrupting Python no longer leads to segfaults (#1601, fixed in #1602).
 
+- Print method for Python callables now includes the callable’s signature (#1605)
+
 - `virtualenv_starter()` no longer warns when encountering broken symlinks (#1598).
 
 # reticulate 1.36.1
 
-- Fix issue where `py_to_r()` method for Pandas DataFrames would error 
-  if `py_to_r()` S3 methods were defined for Pandas subtypes, 
+- Fix issue where `py_to_r()` method for Pandas DataFrames would error
+  if `py_to_r()` S3 methods were defined for Pandas subtypes,
   (as done by {anndata}) (#1591).
-  
+
 - "Python Dependencies" vignette edits (@salim-b, #1586)
 
-- Added an option for extra command-line arguments in 
+- Added an option for extra command-line arguments in
   `conda_create()` and `conda_install()` (#1585).
 
-- Fixed issue where `conda_install()` would ignore user-specified 
+- Fixed issue where `conda_install()` would ignore user-specified
   channels during Python installation (#1594).
 
 # reticulate 1.36.0
diff --git a/R/python.R b/R/python.R
index 1839a9709..1f9b3ccc5 100644
--- a/R/python.R
+++ b/R/python.R
@@ -1,11 +1,72 @@
 
 #' @export
 print.python.builtin.object <- function(x, ...) {
-  writeLines(py_repr(x))
+  formatted <- if (py_is_callable(x))
+    py_format_callable(x, ...)
+  else
+    py_repr(x)
+
+  writeLines(formatted)
   invisible(x)
 }
 
 
+py_format_callable <- function(x, ...) {
+
+  type <- py_to_r(py_get_attr(py_get_attr(x, "__class__"), "__name__"))
+
+  name <- py_to_r(py_get_attr(x, "__qualname__", TRUE) %||%
+                  py_get_attr(x, "__name__", TRUE))
+
+  module <- py_to_r(py_get_attr(x, "__module__", TRUE))
+  if (!is.null(module))
+    name <- paste0(c(module, name), collapse = ".")
+
+  inspect <- import("inspect")
+
+  get_formatted_signature <- function(x, drop_first = FALSE) {
+    tryCatch({
+      sig <- inspect$signature(x)
+      if (drop_first) {
+        # i.e., drop first positional arg, most typically: 'self'
+        #
+        # We only need to do this if inspect.signature() errored on the the
+        # callable itself, but succeeded on callable.__init__. This can happen
+        # for some built-in-C class where methods are slot wrappers.
+        # E.g., builtin exceptions like 'RuntimeError'.
+        sig <- inspect$Signature(
+          parameters = iterate(sig$parameters$values())[-1],
+          return_annotation = sig$return_annotation
+        )
+      }
+
+      formatted <- py_str_impl(sig)
+
+      # split long signatures across multiple lines, so they're readable
+      if (py_len(sig$parameters) >= 4L) {
+        for (formatted_arg in iterate(sig$parameters$values(), py_str_impl))
+          formatted <- sub(formatted_arg,
+                           paste0("\n  ", formatted_arg),
+                           formatted, fixed = TRUE)
+
+        formatted <- sub(", /,", ",\n  /,", formatted, fixed = TRUE) # positional only separator
+        formatted <- sub(", *,", ",\n  *,", formatted, fixed = TRUE) # kw-only separator
+        formatted <- sub("\\)($| ->)", "\n)\\1", formatted) # final closing parens )
+      }
+      formatted
+    },
+    error = function(e) NULL)
+  }
+
+  formatted_sig <- get_formatted_signature(x) %||%
+    get_formatted_signature(py_get_attr(x, "__init__", TRUE), TRUE) %||%
+    get_formatted_signature(py_get_attr(x, "__new__", TRUE), TRUE) %||%
+    "(?)"
+
+  sprintf("<%s %s%s>", type, name, formatted_sig)
+}
+
+
 #' @importFrom utils str
 #' @export
 str.python.builtin.object <- function(object, ...) {
@@ -1761,4 +1822,3 @@ format_py_exception_traceback_with_clickable_filepaths <- function(etb) {
 
   cli::col_silver(hint)
 }
-