Interior of Mars
Until the InSight Mission we only had guesses of what the interior of Mars was like. However, with InSight, we are beginning to get limited data of the interior of Mars. Our information will greatly increase when we have several seismographs on Mars, since we will then have more than one 'view' of Martian earthquakes.
Overview of Layers
Mars' crust is between 24 and 72 km thick. This crust is very light and seems to be highly fractured. The crust of Mars seems enriched in radioactive material, with the core having proportionally less radioactive material than Earth, which results in less heating lower down. 
It has a very deep lithosphere which is close to 500 km thick. Like Earth, as you go deeper the mantle becomes less rigid and softer. The mantle has only one layer, rather than Earth's two layers.
The core of Mars is liquid, and larger than expected at ~1830 km. The core is less dense, at 5.7-6.3 g/cm3, than Earth's at 9.9-12.2 g/cm3 . Likely it has more sulfur, oxygen and even hydrogen than Earth's core. These other elements make the Marian core less conductive than Earth's, which is consistent with Mars' extremely weak magnetic field.