Labyrinth seals are mechanical devices used for sealing turbomachinery equipment in applications such as methane (CH 4 ) and carbon dioxide (CO 2 ) compression. Therefore, the optimization of labyrinth seals is crucial for controlling the increase in temperature of the atmosphere because CH 4 and CO 2 are greenhouse gases (GHGs). In this context, this work aims to develop topology optimization formulations by considering turbulent flow and fluid-structure interaction (FSI) and to apply these formulations to the design of efficient labyrinth seals, reducing GHGs emissions. The main challenges of labyrinth seal topology optimization are avoiding the channel closure, assigning different velocities for the rotor and stator, and avoiding solid islands disconnected from the walls. This work proposes two topology optimization algorithms that attend to these requirements and compare them. The first algorithm is based on binary design variables and one extension of the TOBS method (Topology Optimization of Binary Structures) that avoids undesired material distributions. The second algorithm is based on continuous design variables and one method that considers the fluid channel as the interface between the rotor and stator. This last algorithm requires the use of connectivity constraints to avoid solid islands. Two connectivity constraints are investigated, one based on fluid-structure interaction and the other on a virtual heat transfer problem. The binary and continuous approaches are compared for laminar and turbulent flows. As some designs present material distributions that cannot be assembled directly due to interference between the rotor and stator, this work also investigates the combination of the concepts of labyrinth seals and inflatable seals, which are seals that deform when pressurized. This characteristic may be used to adjust the clearance between the assembled parts and to reach complex assemblies, for example. The labyrinth seal model considers turbulence, which influences labyrinth seal performance. The Reynolds Averaged Navier-Stokes (RANS) equations closed with the Spalart-Allmaras turbulence model are used to model the flow in the labyrinth seal cavity. The inflatable seal design considers the static equilibrium of structures subjected to pressure loads and large deformations. The finite element method (FEM) is used to solve the equilibrium equations. The sensitivity analysis is carried out with automatic differentiation. The optimization problem is solved with the CPLEX ® and MMA (Method of Moving Asymptotes) optimizers. Three labyrinth seal configurations are optimized: straight-through, staggered and stepped. The inflatable seals are designed by topology optimization with pressure loads and large deformations.