The hybrid semiconductor pixel detector Timepix is a successor of the very successful Medipix2 detector. Besides its excellent imaging properties such as high dynamic range, no dark current and single quantum counting, it allows the measurement of particle interaction time and deposited energy in each pixel. These features open up a wide range of new possibilities and application areas. It is apparent that for meaningful utilization of the advantages of the detector, many areas need to be covered starting from the good understanding of the detector behavior and ending with appropriate custom made hardware. This work addresses, solves and improves most of these challenges. New methods of characterization and evaluation of the detector properties, possibilities of new and unique applications as well as development of the new hardware solutions significantly expanding applicability of this outstanding detection device are presented. Evaluation of local radiation damage in silicon sensor via charge collection mapping, position-sensitive spectroscopy of ultra-cold neutrons or development of the Space radiation micro-tracker, these are examples of the work addressed in this Thesis.