Heat exchangers are the cornerstone of many energy and industrial systems. Indeed, thermal conditioning has a trending increasing importance in a large variety of applications ranging from aeronautical, and automotive applications to material shaping processes. This oriented our study towards topology optimization of conjugate heat transfer systems. In addition to maximize the amount of transferred energy, it also focuses on the reduction of pressure drops -through the inclusion of a multi-objective cost function- since head losses are directly related to the operating cost of the hydraulic system. Moreover, studies show that, for multi-channel heat exchangers, the optimization of flow distribution in the upstream parts of the system has a direct positive effect on the core of the system. Thus, flow uniformity also takes part in the optimization process. Finally, for applications involving the benefits of latent heat, and/or for evaporation/condensation processes, multi-phase flows join the modelization, and are also taken into consideration. An in-house implementation of the variational multiscale stabilized finite element method is used for benchmarking and numerical experimentation. The interface between the solid and fluid regions is described by a truncated level-set, suitable to be transported by a single step advection solver that guaranties accuracy for a minimal computational cost. The continuous adjoint method is used for sensitivity computation. Space varying material properties, allows the representation of both the fluid and solid regions on the same grid, so the domain is considered as a whole when computing the governing and adjoint equations. Finally, anisotropic mesh adaptation is applied for precisely meshing our regions of interest -here the interface, where the nearest elements are highly stretched. In addition to reducing the computational cost, mesh adaptation assured a smooth deformation of the interface, both by advection or by enforced geometrical constraints . For several cases involving competition between heat transfer enhancement, pressure drop reduction, and flow distribution, this numerical framework has been found to yield accurate and non-intuitive results while maintaining the CPU cost affordable. We will discuss the main results obtained in 2-D and 3-D, and will present novel designs obtained for an industrial application.