A process allowing treatment of effluents. The process comprises the following steps: (a) providing a reactor comprising an inlet, an outlet, at least one block of electrodes comprising at least one anode and at least one cathode. The effluent to be treated is run between the electrodes in an upward direction; and (b) allowing the effluent to be treated to run between the electrodes of the at least one block in an upward direction so as to submit the effluent to an electrical current and thereby treating the effluent by electrocoagulation and/or electroflotation. There is thus produced a sludge containing at least one pollutant that is comprised in the effluent to be treated, and a treated effluent. The produced sludge is thereafter separated from the treated effluent. There is also provided an apparatus allowing implementation of this process. The process and the apparatus make it possible to efficiently treat effluents of various compositions and that may contain a wide range of contaminants.