diff --git a/dvc/commands/experiments/pull.py b/dvc/commands/experiments/pull.py
--- a/dvc/commands/experiments/pull.py
+++ b/dvc/commands/experiments/pull.py
@@ -3,23 +3,13 @@
 
 from dvc.cli.command import CmdBase
 from dvc.cli.utils import append_doc_link
-from dvc.exceptions import InvalidArgumentError
 from dvc.ui import ui
 
 logger = logging.getLogger(__name__)
 
 
 class CmdExperimentsPull(CmdBase):
-    def raise_error_if_all_disabled(self):
-        if not any([self.args.experiment, self.args.all_commits, self.args.rev]):
-            raise InvalidArgumentError(
-                "Either provide an `experiment` argument, or use the "
-                "`--rev` or `--all-commits` flag."
-            )
-
     def run(self):
-        self.raise_error_if_all_disabled()
-
         pulled_exps = self.repo.experiments.pull(
             self.args.git_remote,
             self.args.experiment,
diff --git a/dvc/commands/experiments/push.py b/dvc/commands/experiments/push.py
--- a/dvc/commands/experiments/push.py
+++ b/dvc/commands/experiments/push.py
@@ -5,20 +5,12 @@
 from dvc.cli import completion
 from dvc.cli.command import CmdBase
 from dvc.cli.utils import append_doc_link
-from dvc.exceptions import InvalidArgumentError
 from dvc.ui import ui
 
 logger = logging.getLogger(__name__)
 
 
 class CmdExperimentsPush(CmdBase):
-    def raise_error_if_all_disabled(self):
-        if not any([self.args.experiment, self.args.all_commits, self.args.rev]):
-            raise InvalidArgumentError(
-                "Either provide an `experiment` argument, or use the "
-                "`--rev` or `--all-commits` flag."
-            )
-
     @staticmethod
     def log_result(result: Dict[str, Any], remote: str):
         from dvc.utils import humanize
@@ -59,8 +51,6 @@ def join_exps(exps):
     def run(self):
         from dvc.repo.experiments.push import UploadError
 
-        self.raise_error_if_all_disabled()
-
         try:
             result = self.repo.experiments.push(
                 self.args.git_remote,
diff --git a/dvc/repo/experiments/pull.py b/dvc/repo/experiments/pull.py
--- a/dvc/repo/experiments/pull.py
+++ b/dvc/repo/experiments/pull.py
@@ -21,7 +21,7 @@
 def pull(  # noqa: C901
     repo,
     git_remote: str,
-    exp_names: Union[Iterable[str], str],
+    exp_names: Optional[Union[Iterable[str], str]] = None,
     all_commits=False,
     rev: Optional[Union[List[str], str]] = None,
     num=1,
@@ -32,30 +32,30 @@ def pull(  # noqa: C901
     exp_ref_set: Set["ExpRefInfo"] = set()
     if all_commits:
         exp_ref_set.update(exp_refs(repo.scm, git_remote))
+    elif exp_names:
+        if isinstance(exp_names, str):
+            exp_names = [exp_names]
+        exp_ref_dict = resolve_name(repo.scm, exp_names, git_remote)
+
+        unresolved_exp_names = []
+        for exp_name, exp_ref in exp_ref_dict.items():
+            if exp_ref is None:
+                unresolved_exp_names.append(exp_name)
+            else:
+                exp_ref_set.add(exp_ref)
+
+        if unresolved_exp_names:
+            raise UnresolvedExpNamesError(unresolved_exp_names)
+
     else:
-        if exp_names:
-            if isinstance(exp_names, str):
-                exp_names = [exp_names]
-            exp_ref_dict = resolve_name(repo.scm, exp_names, git_remote)
-
-            unresolved_exp_names = []
-            for exp_name, exp_ref in exp_ref_dict.items():
-                if exp_ref is None:
-                    unresolved_exp_names.append(exp_name)
-                else:
-                    exp_ref_set.add(exp_ref)
-
-            if unresolved_exp_names:
-                raise UnresolvedExpNamesError(unresolved_exp_names)
-
-        if rev:
-            if isinstance(rev, str):
-                rev = [rev]
-            rev_dict = iter_revs(repo.scm, rev, num)
-            rev_set = set(rev_dict.keys())
-            ref_info_dict = exp_refs_by_baseline(repo.scm, rev_set, git_remote)
-            for _, ref_info_list in ref_info_dict.items():
-                exp_ref_set.update(ref_info_list)
+        rev = rev or "HEAD"
+        if isinstance(rev, str):
+            rev = [rev]
+        rev_dict = iter_revs(repo.scm, rev, num)
+        rev_set = set(rev_dict.keys())
+        ref_info_dict = exp_refs_by_baseline(repo.scm, rev_set, git_remote)
+        for _, ref_info_list in ref_info_dict.items():
+            exp_ref_set.update(ref_info_list)
 
     pull_result = _pull(repo, git_remote, exp_ref_set, force)
 
diff --git a/dvc/repo/experiments/push.py b/dvc/repo/experiments/push.py
--- a/dvc/repo/experiments/push.py
+++ b/dvc/repo/experiments/push.py
@@ -97,7 +97,7 @@ def exp_refs_from_rev(scm: "Git", rev: List[str], num: int = 1) -> Set["ExpRefIn
 def push(
     repo: "Repo",
     git_remote: str,
-    exp_names: Union[List[str], str],
+    exp_names: Optional[Union[List[str], str]] = None,
     all_commits: bool = False,
     rev: Optional[Union[List[str], str]] = None,
     num: int = 1,
@@ -111,7 +111,8 @@ def push(
         exp_ref_set.update(exp_refs(repo.scm))
     if exp_names:
         exp_ref_set.update(exp_refs_from_names(repo.scm, ensure_list(exp_names)))
-    if rev:
+    else:
+        rev = rev or "HEAD"
         if isinstance(rev, str):
             rev = [rev]
         exp_ref_set.update(exp_refs_from_rev(repo.scm, rev, num=num))

Also, `dvc exp push origin --rev HEAD` seems to be not working on CI. I didn't manage to make it work the last time I tried (I didn't have enough time unfortunately). It comes down to the supported E2E scenarios and making sure that they are not broken / fairly simple to use.
@shcheklein Added a separate ticket to discuss the more general problem.
diff --git a/tests/func/experiments/test_remote.py b/tests/func/experiments/test_remote.py
--- a/tests/func/experiments/test_remote.py
+++ b/tests/func/experiments/test_remote.py
@@ -35,6 +35,9 @@ def test_push(tmp_dir, scm, dvc, git_upstream, exp_stage, use_url):
     dvc.experiments.push(remote, [ref_info1.name])
     assert git_upstream.tmp_dir.scm.get_ref(str(ref_info1)) == exp1
 
+    dvc.experiments.push(remote)
+    assert git_upstream.tmp_dir.scm.get_ref(str(ref_info3)) == exp3
+
 
 @pytest.mark.parametrize("all_,rev,result3", [(True, False, True), (False, True, None)])
 def test_push_args(tmp_dir, scm, dvc, git_upstream, exp_stage, all_, rev, result3):
@@ -173,6 +176,11 @@ def test_list_remote(tmp_dir, scm, dvc, git_downstream, exp_stage, use_url):
 def test_pull(tmp_dir, scm, dvc, git_downstream, exp_stage, use_url):
     from dvc.exceptions import InvalidArgumentError
 
+    # fetch and checkout to downstream so both repos start from same commit
+    downstream_repo = git_downstream.tmp_dir.scm.gitpython.repo
+    fetched = downstream_repo.remote(git_downstream.remote).fetch()
+    downstream_repo.git.checkout(fetched)
+
     remote = git_downstream.url if use_url else git_downstream.remote
     downstream_exp = git_downstream.tmp_dir.dvc.experiments
     with pytest.raises(InvalidArgumentError):
@@ -200,6 +208,9 @@ def test_pull(tmp_dir, scm, dvc, git_downstream, exp_stage, use_url):
     downstream_exp.pull(remote, [str(ref_info1)])
     assert git_downstream.tmp_dir.scm.get_ref(str(ref_info1)) == exp1
 
+    downstream_exp.pull(remote)
+    assert git_downstream.tmp_dir.scm.get_ref(str(ref_info3)) == exp3
+
 
 @pytest.mark.parametrize("all_,rev,result3", [(True, False, True), (False, True, None)])
 def test_pull_args(tmp_dir, scm, dvc, git_downstream, exp_stage, all_, rev, result3):
diff --git a/tests/unit/command/test_experiments.py b/tests/unit/command/test_experiments.py
--- a/tests/unit/command/test_experiments.py
+++ b/tests/unit/command/test_experiments.py
@@ -294,12 +294,7 @@ def test_experiments_push(dvc, scm, mocker):
     )
     cmd = cli_args.func(cli_args)
 
-    with pytest.raises(InvalidArgumentError) as exp_info:
-        cmd.run()
-    assert (
-        str(exp_info.value) == "Either provide an `experiment` argument"
-        ", or use the `--rev` or `--all-commits` flag."
-    )
+    assert cmd.run() == 0
 
 
 def test_experiments_pull(dvc, scm, mocker):
@@ -351,12 +346,7 @@ def test_experiments_pull(dvc, scm, mocker):
     )
     cmd = cli_args.func(cli_args)
 
-    with pytest.raises(InvalidArgumentError) as exp_info:
-        cmd.run()
-    assert (
-        str(exp_info.value) == "Either provide an `experiment` argument"
-        ", or use the `--rev` or `--all-commits` flag."
-    )
+    assert cmd.run() == 0
 
 
 def test_experiments_remove_flag(dvc, scm, mocker, capsys, caplog):

exp push: default to `--rev HEAD`
Let's make `dvc exp push origin` push all experiments derived from the HEAD revision by default. This is especially useful in CI, where it's common to want to push the latest experiment and `dvc exp push origin --rev HEAD` feels like it's too complicated.

See discussion in https://iterativeai.slack.com/archives/C01116VLT7D/p1686321601633079.

tests/unit/command/test_experiments.py::test_experiments_push tests/unit/command/test_experiments.py::test_experiments_pull
tests/unit/command/test_experiments.py::test_experiments_list tests/func/experiments/test_remote.py::test_auth_error_pull tests/unit/command/test_experiments.py::test_experiments_show tests/unit/command/test_experiments.py::test_experiments_diff_revs tests/unit/command/test_experiments.py::test_experiments_diff tests/unit/command/test_experiments.py::test_experiments_remove_special tests/unit/command/test_experiments.py::test_experiments_list_format[args2-sha-a\n] tests/unit/command/test_experiments.py::test_experiments_remove_flag tests/unit/command/test_experiments.py::test_experiments_list_format[args0-main:\n\tsha-a tests/unit/command/test_experiments.py::test_experiments_branch tests/unit/command/test_experiments.py::test_experiments_remove_invalid tests/unit/command/test_experiments.py::test_experiments_list_remote tests/unit/command/test_experiments.py::test_experiments_run tests/unit/command/test_experiments.py::test_experiments_save tests/unit/command/test_experiments.py::test_experiments_clean tests/unit/command/test_experiments.py::test_experiments_apply tests/unit/command/test_experiments.py::test_experiments_list_format[args1-exp-a\n]