diff --git a/backend/onedrive/api/types.go b/backend/onedrive/api/types.go
index 346829afa..53140819c 100644
--- a/backend/onedrive/api/types.go
+++ b/backend/onedrive/api/types.go
@@ -410,3 +410,28 @@ func (i *Item) GetParentReference() *ItemReference {
 func (i *Item) IsRemote() bool {
 	return i.RemoteItem != nil
 }
+
+// User details for each version
+type User struct {
+	Email       string `json:"email"`
+	ID          string `json:"id"`
+	DisplayName string `json:"displayName"`
+}
+
+// LastModifiedBy for each version
+type LastModifiedBy struct {
+	User User `json:"user"`
+}
+
+// Version info
+type Version struct {
+	ID                   string         `json:"id"`
+	LastModifiedDateTime time.Time      `json:"lastModifiedDateTime"`
+	Size                 int            `json:"size"`
+	LastModifiedBy       LastModifiedBy `json:"lastModifiedBy"`
+}
+
+// VersionsResponse is returned from /versions
+type VersionsResponse struct {
+	Versions []Version `json:"value"`
+}
diff --git a/backend/onedrive/onedrive.go b/backend/onedrive/onedrive.go
index ea4007b79..13cb10aa0 100755
--- a/backend/onedrive/onedrive.go
+++ b/backend/onedrive/onedrive.go
@@ -14,6 +14,7 @@ import (
 	"path"
 	"strconv"
 	"strings"
+	"sync"
 	"time"
 
 	"github.com/pkg/errors"
@@ -26,6 +27,8 @@ import (
 	"github.com/rclone/rclone/fs/config/obscure"
 	"github.com/rclone/rclone/fs/fserrors"
 	"github.com/rclone/rclone/fs/hash"
+	"github.com/rclone/rclone/fs/operations"
+	"github.com/rclone/rclone/fs/walk"
 	"github.com/rclone/rclone/lib/atexit"
 	"github.com/rclone/rclone/lib/dircache"
 	"github.com/rclone/rclone/lib/encoder"
@@ -1275,6 +1278,73 @@ func (f *Fs) PublicLink(ctx context.Context, remote string, expire fs.Duration,
 	return result.Link.WebURL, nil
 }
 
+// CleanUp deletes all the hidden files.
+func (f *Fs) CleanUp(ctx context.Context) error {
+	token := make(chan struct{}, fs.Config.Checkers)
+	var wg sync.WaitGroup
+	err := walk.Walk(ctx, f, "", true, -1, func(path string, entries fs.DirEntries, err error) error {
+		err = entries.ForObjectError(func(obj fs.Object) error {
+			o, ok := obj.(*Object)
+			if !ok {
+				return errors.New("internal error: not a onedrive object")
+			}
+			wg.Add(1)
+			token <- struct{}{}
+			go func() {
+				defer func() {
+					<-token
+					wg.Done()
+				}()
+				err := o.deleteVersions(ctx)
+				if err != nil {
+					fs.Errorf(o, "Failed to remove versions: %v", err)
+				}
+			}()
+			return nil
+		})
+		wg.Wait()
+		return err
+	})
+	return err
+}
+
+// Finds and removes any old versions for o
+func (o *Object) deleteVersions(ctx context.Context) error {
+	opts := newOptsCall(o.id, "GET", "/versions")
+	var versions api.VersionsResponse
+	err := o.fs.pacer.Call(func() (bool, error) {
+		resp, err := o.fs.srv.CallJSON(ctx, &opts, nil, &versions)
+		return shouldRetry(resp, err)
+	})
+	if err != nil {
+		return err
+	}
+	if len(versions.Versions) < 2 {
+		return nil
+	}
+	for _, version := range versions.Versions[1:] {
+		err = o.deleteVersion(ctx, version.ID)
+		if err != nil {
+			return err
+		}
+	}
+	return nil
+}
+
+// Finds and removes any old versions for o
+func (o *Object) deleteVersion(ctx context.Context, ID string) error {
+	if operations.SkipDestructive(ctx, fmt.Sprintf("%s of %s", ID, o.remote), "delete version") {
+		return nil
+	}
+	fs.Infof(o, "removing version %q", ID)
+	opts := newOptsCall(o.id, "DELETE", "/versions/"+ID)
+	opts.NoResponse = true
+	return o.fs.pacer.Call(func() (bool, error) {
+		resp, err := o.fs.srv.Call(ctx, &opts)
+		return shouldRetry(resp, err)
+	})
+}
+
 // ------------------------------------------------------------
 
 // Fs returns the parent Fs
@@ -1840,6 +1910,7 @@ var (
 	_ fs.DirCacheFlusher = (*Fs)(nil)
 	_ fs.Abouter         = (*Fs)(nil)
 	_ fs.PublicLinker    = (*Fs)(nil)
+	_ fs.CleanUpper      = (*Fs)(nil)
 	_ fs.Object          = (*Object)(nil)
 	_ fs.MimeTyper       = &Object{}
 	_ fs.IDer            = &Object{}
diff --git a/docs/content/onedrive.md b/docs/content/onedrive.md
index 8a6e3d12d..ab91acb18 100644
--- a/docs/content/onedrive.md
+++ b/docs/content/onedrive.md
@@ -331,6 +331,8 @@ This counts against a users quota.
 For example changing the modification time of a file creates a second
 version, so the file is using twice the space.
 
+You can use the `rclone cleanup` command (see below) to remove old versions.
+
 The `copy` is the only rclone command affected by this as we copy
 the file and then afterwards set the modification time to match the
 source file.
@@ -359,6 +361,18 @@ Note: This will disable the creation of new file versions, but will not remove a
 8. Use rclone to upload or modify files. (I also use the --no-update-modtime flag)
 9. Restore the versioning settings after using rclone. (Optional)
 
+### Cleanup
+
+OneDrive supports `rclone cleanup` which causes rclone to look through
+every file under the path supplied and delete all version but the
+current version. Because this involves traversing all the files, then
+querying each file for versions it can be quite slow. Rclone does
+`--checkers` tests in parallel. The command also supports `-i` which
+is a great way to see what it would do.
+
+    rclone cleanup -i remote:path/subdir # interactively remove all old version for path/subdir
+    rclone cleanup remote:path/subdir    # unconditionally remove all old version for path/subdir
+
 ### Troubleshooting ###
 
 #### Unexpected file size/hash differences on Sharepoint ####
diff --git a/docs/content/overview.md b/docs/content/overview.md
index 5cc94d156..f45a3bd88 100644
--- a/docs/content/overview.md
+++ b/docs/content/overview.md
@@ -336,7 +336,7 @@ operations more efficient.
 | Mega                         | Yes   | No   | Yes  | Yes     | Yes     | No    | No           | No [#2178](https://github.com/rclone/rclone/issues/2178) | Yes | Yes |
 | Memory                       | No    | Yes  | No   | No      | No      | Yes   | Yes          | No          | No | No |
 | Microsoft Azure Blob Storage | Yes   | Yes  | No   | No      | No      | Yes   | Yes          | No [#2178](https://github.com/rclone/rclone/issues/2178) | No  | No |
-| Microsoft OneDrive           | Yes   | Yes  | Yes  | Yes     | No [#575](https://github.com/rclone/rclone/issues/575) | No | No | Yes | Yes | Yes |
+| Microsoft OneDrive           | Yes   | Yes  | Yes  | Yes     | Yes     | No    | No           | Yes | Yes | Yes |
 | OpenDrive                    | Yes   | Yes  | Yes  | Yes     | No      | No    | No           | No                                                    | No  | Yes |
 | OpenStack Swift              | Yes † | Yes  | No   | No      | No      | Yes   | Yes          | No [#2178](https://github.com/rclone/rclone/issues/2178) | Yes | No |
 | pCloud                       | Yes   | Yes  | Yes  | Yes     | Yes     | No    | No           | Yes | Yes | Yes |