the light cone
Stand at an event — a point in spacetime, a 'here and now'. Which other events could you have caused, and which could have caused you? The light cone draws the answer as geometry: the double cone swept out by all light rays passing through that event, dividing spacetime into your absolute future, your absolute past, and the 'elsewhere' you can neither affect nor be affected by.
In coordinates centered on the event, the light cone is the set of points with zero interval, ds^2 = c^2 t^2 - x^2 - y^2 - z^2 = 0, i.e. r = c|t| — a cone opening at 45 degrees when the axes are scaled so light travels at unit slope. Its interior splits into the future cone (t>0, time-like, ds^2>0) and the past cone (t<0); the exterior is space-like (ds^2<0). Because ds^2 is Lorentz invariant, every inertial observer agrees on which region an event lies in — so the cone is absolute even though 'space' and 'time' separately are not.
The light cone is the geometric statement of causality: a cause and its effect must be joined by a time-like or null (light-like) curve lying inside or on the cone, since no signal outruns light. Two events with space-like separation have no invariant time order — different observers disagree on which came first — which is precisely why they cannot be causally linked. Common misconception: the cone is not a cone 'in space' but in spacetime; its cross-section at a fixed time is an expanding sphere of light.
A supernova 1000 light-years away that reaches our telescopes tonight actually exploded about 1000 years ago; the explosion event sits on our past light cone. Anything happening at that star 'right now' lies outside our light cone — causally inaccessible until its light arrives centuries hence.
We can only ever see events on or inside our past light cone.
'Inside the cone' versus 'on the cone' matters: massive particles move on time-like worldlines strictly inside their future cones, while light and massless particles travel exactly on the cone (null worldlines). Nothing physical travels outside it.