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We present a set of complementary experimental and numerical tools for studying miscible fluid displacements in porous media with large scale heterogeneities. Experiments are realized in transparent 2D Hele-Shaw cells allowing optical observations and in 3D packings of glass beads with an acoustical technique for imaging fluid displacements. Permeability heterogeneities are modeled by spatial variations of either the local aperture of the Hele-Shaw cell or the diameter of the grains used in the packing. The Hele-Shaw cell model provides high resolution maps of the invasion front location at regular time intervals and of the flow lines: the velocity field is determined by combining these informations. Acoustical images of relative concentration distributions in the 3D packing are in agreement with Hele-Shaw cell data and can be obtained in a broader range of experimental situations. Such experiments realized with a stabilizing density contrast between invading and displaced fluids demonstrate a strong reduction of the front width at low flow velocities, a similar reduction is obtained at high velocities with a stabilizing viscosity contrast. The technique is also applicable to study fluid displacements in natural opaque media. Numerical simulations by a Boltzmann lattice technique using a Stokes-like diffusive term to smooth out the effect of permeability discontinuities provide complementary informations. They are shown to give similar results as experiments for same flow parameter values and to allow for a fast exploration of a broad range of fluid properties and flow situations.