A review is given of numerical, analytical, and experimental research regarding the two-way coupling effect between particles and fluid turbulence in a homogeneous, isotropic turbulent suspension. The emphasis of this review is on the effect of the suspended particles on the spectrum of the carrier fluid, in order to explain the physical mechanisms that are involved. An important result of numerical simulations and analytical models (neglecting the effect of gravity) is that, for a homogeneous and isotropic suspension with particles with a response time much larger than the Kolmogorov time scale, the main effect of the particles is suppression of the energy of eddies of all sizes. However for a suspension with particles with a response time comparable to or smaller than the Kolmogorov time, the Kolmogorov length scale will decrease and the turbulence energy of (nearly) all eddy sizes increases. For a suspension with particles with a response time in between the two limiting cases mentioned above the energy of the larger eddies is suppressed, whereas the energy of the smaller ones is enhanced. Attention is paid to several physical mechanisms that were suggested in the literature to explain this influence of the particles on the turbulence. In some of the experimental studies, certain results from simulations and models have, indeed, been confirmed. However, in other experiments these results were not found. This is attributed to the role of gravity, which leads to turbulence production by the particles. Additional research effort is needed to fully understand the physical mechanisms causing the two-way coupling effect in a homogeneous, isotropic, and turbulently flowing suspension. This review contains 47 references.