The interior of the horizon is well described using appropriately chosen metrics, e.g., the Kruskal-Szekeres metric that describes the black hole from the perspective of an infalling observer. Insofar as that observer is concerned, the interior is not any different from the outside. As the observer approaches the black hole, tidal forces can become very large, though seemingly paradoxically, the bigger the black hole, the smaller the tidal force; so as you approach the horizon of, say, a galaxy-sized supermassive black hole, there would be no significant tidal forces near the horizon. And as you cross the horizon... well, nothing special happens. Life goes on as normal, at least for a while. There is one difference. An observer outside the black hole can, if in possession of a powerful enough rocket, accelerate away to infinity. An observer who crossed the horizon is doomed to fall into the singularity. And the more you struggle, the faster you reach your doom, so the best thing to do is to not accelerate. As you approach the singularity, tidal forces will grow beyond limit, so you'd be ripped apart. Eventually, the gravitational force (in particular, tidal forces) will become comparable in magnitude to other (electromagnetic, nuclear) forces, and that's where our understanding ends: to describe what happens (and indeed, if there is actually a singularity or something else) would require a valid theory of quantum gravity, which we do not have.

Toth and Rakhshan thanks you for your answers. I like to discuss a little more about it. For example, the description of Kruskal-Szekeres still considers the mass of the black hole as a  mass point at the geometric center of the spatial region assigned to it. If the mass density is large (almost infinite) gravitational field is huge, and in GR, being a local theory where a tangent plane and normal coordinates must assumed to describe physical phenomena, how can we talk about phenomena "Euclidean" as tidal forces.

Allow me to clarify a few things.

First, Kruskal-Szekeres is just a convenient choice of coordinates that allows one to cover both the interior and the exterior of a Schwarzschild horizon with a single coordinate chart. So it is not a new theory; the theory is still the same old Schwarzschild solution.

Second, the Schwarzschild solution is a spherically symmetric, static vacuum solution. There are no masses involved. The solution is singular at the origin, and it is characterized by a parameter that, in the weak field limit, corresponds to the Newtonian potential of an object with a corresponding mass. On the other hand, Birkhoff's theorem tells us that it is also the correct solution describing the metric outside any spherically symmetric mass. But the solution says nothing about that mass; it only describes the gravitational field in the vacuum surrounding the mass.

Third, regarding what happens when there are actual masses involved, the interior of a collapsing object is described by the solution first published by Oppenheimer and Snyder in 1939. This solution remains applicable so long as pressure can be neglected and, well, so long as gravity itself remains weak when compared to other forces. When the gravitational field is huge, quantum gravitational effects can no longer be neglected, and that's where our understanding ends... in the absence of a viable theory of gravity, we can only guess what happens.