The following keyboard shortcuts are available in both iOS and OSX versions (unless indicated otherwise.)

NB: iOS requires bluetooth keyboard

TAB Create a new child
RETURN End edit or create new sibling
⌘ RETURN Start edit or create a new sibling (splitting the text at the cursor if necessary)
Shift RETURN Create a new sibling (before)
⌥ RETURN Insert newline into topic text
Shift TAB Create new parent
F2 [OSX only] Edit selected topic text
PERIOD Show/Hide a branch
[0..9] Show N levels or sub topic deep
⌘ [1..5] Set topic priority
⌥ [1..9] Add nth favourite icon
SPACE Show QuickLook (images/attachments)
ESC Abort edit and revert to original text or deselect all. Undo is available to recover any reverted text.
⌘ A Select All (visible) topics
Arrow Key Navigate around the map (topic to topic)
⌘ Arrow Key Change topic order
⌥ Arrow Key Nudge manual aligned topic positions
⌘ ⌥ Arrow Key Create new related floating topics
⌘ [X C V] Cut/ Copy/ Paste
BACKSPACE Delete selected topics (including child topics)
⌘ BACKSPACE Delete individual (selected) topics (not including child topics)
⌘ +/- Increase/decrease size (image, font etc.)
⌘ [B I U] Bold/ Italic/ Underline
⌘ ⌥ U Strikethrough
⌘ F [OSX only] Find/Replace
⌘ ⌥ T Toggle between edit and view mode for notes
⌘ Shift T Toggle the notes window open/closed
⌘ Ctrl T Toggle between editing note and topic text
⌘ R Research - launch browser with topic text as search term
⌘ Ctrl F Toggle 'full screen' mode
⌘ Shift K Insert Callout topic
L [OSX only] Create relationship between 2 selected topics
⌘ 0 Toggle between 'Zoom to fit map' and 'Center map with no zoom'
⌘ Shift 0 Toggle between 'Zoom to fit map' and 'Zoom to fit selection'
⌘ Ctrl 0 Toggle 'auto zoom' on/off
⌘ > Zoom in
⌘ < Zoom out
P Increment the Progress attribute (Shift P to decrement)
⌘ K [OSX only] Edit the hyperlink attribute
⌘ ⌥ K Open the hyperlink
⌘ Shift F Toggle Focus mode on/off
DoubleClick Canvas Create new floating topic (DoubleTap on iOS)
CMD+DoubleClick Canvas Create new related floating topic (SHIFT+DoubleTap on iOS)
CMD+DoubleClick Topic Create new relationship (SHIFT+DoubleTap on iOS)