One of the most fundamental concepts in Star Trek is that of subspace. In the Star Trek world, subspace is an integral part of the space-time continuum - a distinct dimension in space, yet coexistent with 'normal' space. Subspace and normal space are confluenced together. It is the feature of space-time which facilitates faster-than-light transit, in the form of interstellar travel and the transmission of information almost instantaneously over long distances. Many spatial anomalies and astrophysical objects in Star Trek can be found in subspace or be formed in normal space by it. Subspace apparently has an infinite number of domains. Geordi La Forge compared it with "...a huge honeycomb with an infinite number of cells". (TNG: "Schisms").

Exactly what subspace is has never been explicitly revealed on screen in Star Trek. This is not surprising since it is used as a solution and cause of various normally insurmountable problems throughout the series.

Unfortunately, there is no real astrophysical concept actually called subspace. The term 'subspace' is mostly used in mathematics. In linear algebra, a Euclidean subspace (or subspace of Rn) is a set of vectors that is closed under addition and scalar multiplication. Geometrically, a subspace is a flat in n-dimensional Euclidean space that passes through the origin. Examples of subspaces include the solution set to a homogeneous system of linear equations, the subset of Euclidean space described by a system of homogeneous linear parametric equations, the span of a collection of vectors, and the null space, column space, and row space of a matrix. In topology and related areas of mathematics, a subspace of a topological space X is a subset S of X which is equipped with a natural topology induced from that of X called the subspace topology (or the relative topology, or the induced topology, or the trace topology).

However, something akin to subspace or faster-than-light communication might be possible if a theory reported by Fabrice Petit of the Belgian Ceramic Research Centre and Michael Sarrazin of the Facultés Universitaires Notre-Dame de la Paix, in Belgium, in September 2007 in the journal Physical Review D, proves to be true. These researchers describe what amount to shortcuts through extra dimensions.

Petit and Sarrazin, inspired by string theory, describe a situation in which the universe we know is actually just one sheet or brane in a higher dimensional spacetime. In this model of reality, our universe includes a second sheet that we're not normally aware of because we're confined to our own sheet. Petit and Sarrazin describe a specific "braneworld" scenario in which there are just these two branes. In this case, although particles can't exist between branes, they can travel back and forth between the sheets by way of quantum mechanical tunneling, which allows passage across barriers that classical physics considers insurmountable. Under the right circumstances, a powerful magnetic field can cause a particle to oscillate between the two branes. If the other brane is warped in a certain way, distances there may be shorter than in our own brane. This means if a fast-moving particle were made to travel in the other brane for a while before returning to ours, it could actually get to a distant part of our universe much faster than a light signal confined to our brane.

Petit and Sarrazin point out that their theory only works for fermions – particles that include protons and neutrons, but not all types of atoms. Since our bodies contain a lot of atoms that are not fermions, humans could probably never take such shortcuts. But by making electrons or other fermionic particles take shortcuts through the other brane, it might be possible to communicate faster than light speed, just like in Star Trek. Breaking the light speed barrier is normally thought to be impossible because it allows particles to time travel, leading to problems with causality – paradoxes that spring up when effects can happen before their causes. The Petit-Sarrazin scenario needn't violate causality because the shortcutting particles get to their destination faster than light only when confined to our brane. When their path through the extra dimension is taken into account, they actually obey an overall speed limit, allowing causality to be preserved.