Quantum theory of gravity aims to describe quantum properties of the gravitational interaction, which are expected to become relevant at the Planck scale. Unfortunately, despite almost one hundred years of research and significant theoretical progress, no complete and generally accepted theory of the Planck scale physics exists. The most important reason for this status quo is that the expected effects of quantum gravity are extremely subtle and so far have not been confidently observed. Nevertheless, theoretical investigations are constantly pushing our understanding of the Planck scale physics forward, leading to new interesting predictions, which may one day be verified by empirical tests. Our activity in the exploration of Planck scale physics is devoted mostly to such approaches as: Loop Quantum Gravity, Loop Quantum Cosmology, Causal Dynamical Triangulations and deformations of spacetime symmetries (which are usually associated with noncommutative geometry).