A modern context is provided by theoretical physics in which reality is modelled by assuming that all particles follow trajectories- known as worldlines- through a four-dimensional spacetime. Particles in Special Relativity are typically modelled as being point-like, so they move along their worldline occupying an infinitesimally short segment of it. Now, in that context, is simply the time coordinate associated with the infinitesimally short segment of worldline occupied by the particle. Now, therefore, is analogous to 'here' in that it refers to the place where the particle happens to be. The section of the word line leading up to that point is called the past of the particle, and the extrapolated section ahead of that point is the possible future of the particle.
There is still work to be done to make that model consistent with the other main model of theoretical physics, which is quantum theory, in which the positions of particles are not so well-defined.
Since, as far as we know, people are made of particles, here and now for a person is the relatively localised point in spacetime they happen to occupy. The future is a region of spacetime you have yet to enter, while the past is the region you have left.
I have not yet encountered any branch of physics which specifically explores implications of the possibility that particles, or larger objects comprised of them, have extents in time in the same way as they have non-zero extents in space.