The thesis analyzes the interaction region of the Large Hadron Collider (LHC). It proposes, studies and compares several upgrade options. The interaction region is the part of the LHC that hosts the particle detectors which analyze the collisions. An upgrade of the interaction region can potentially increase the number of collision events and therefore it is possible to accumulate and study a larger set of experimental data. The main object of study are the focus systems that consist of a set of magnets in charge of concentrating the particle beams in a small spot at the interaction points. The thesis uses the methods of beam optics and beam dynamics to design new interaction regions. Two design schemes are compared with a detailed analysis of the performance of several implementations. The design of the layouts takes into account the technical limitations that will affect possible realizations. Either analytical or numerical methods are used to evaluate the performance of the proposed layouts. The thesis presents new general methods that can be used for problems beyond the scope of the thesis. An analytical method has been developed for finding the intrinsic limitations of the focus systems. It allows to perform an exhaustive scan of the accessible parameter space and thus presents an efficient tool for guiding the design process. A numerical optimization routine and several enhancements have been implemented in MADX, a code for beam optics design. The routines simplify the solution of several optimization problems of beam optics.