An overview of previous researches related to the problem of flow around a bluff-body, using experimental and numerical methods, is presented in the paper. Experimental investigation was performed by a laser doppler anemometer, measuring velocity components of the water flow around a smooth sphere, and a sphere with dimples in square channels. Measurement results in subcritical velocity flow field, velocity fluctuation components, lift, drag and pressure coefficients, and 2-D Reynolds stress at quasi-stationary flow are conducted using 1-D laser doppler anemometer probe. The obtained experimental results are compared with numerical simulations, which are performed using the ANSYS-CFX software. For the numerical simulations of quasi-steady-state flow, k-ω turbulent model was used, while for numerical simulation of unsteady fluid-flow and for the comparison of results related to the eddy structures, vortex shedding and Reynolds stresses, detached eddy simulation were used. Since the obtained results of experimental and numerical investigation of flow around smooth sphere and sphere with dimples showed good agreement, the considered flow problem was expanded by introducing the influence of a transverse magnetic field with a slight modification of the electrical conductivity of the working fluid. The other physical properties of the fluid remained the same, which also corresponds to realistically possible physical conditions. Numerical simulations were performed for three different values of Hartmann number and very small values of Reynolds magnetic number (inductionless approximation). Comparisons and analyzes of the results were made for the cases containing a magnetic field and those with an absence of a magnetic field.