We discuss the effects of turbulence on the mean Lorentz force and the resulting formation of large-scale magnetic structures. A suppression of turbulent pressure by a large-scale (mean) magnetic field is one of the main reasons for formation of large-scale inhomogeneous magnetic structures in stratified turbulence. This effect mimics a negative effective (mean-field) magnetic pressure owing to a negative contribution of turbulence to the mean magnetic pressure. Under suitable conditions, this phenomenon leads to the negative effective magnetic pressure instability (NEMPI), which can cause the formation of loop-like magnetic structures concentrated at the top of the stratified layer.  In three dimensions these structures resemble the appearance of bipolar magnetic regions in the Sun. This phenomenon was predicted theoretically and detected in direct numerical simulations (DNS) of both, forced stratified turbulence and turbulent convection. DNS requires a significant scale separation to overcome the effect of turbulent diffusion. To study NEMPI analytically and numerically, we also used mean-field magnetohydrodynamics in a parameter regime in which the properties of NEMPI have been found to agree with properties of direct numerical simulations. The results of DNS and mean-field numerical modeling are in good agreement with theoretical predictions.