The invention relates to an apparatus for brewing a drink, such as coffee. The apparatus comprises a chamber (3) for accommodating a mixture of water and a ground product, such as coffee, to be extracted, the chamber having a perforated base (2) on which a strip of filter material (8) can be laid. Means (14,26) are fitted on one side of said base for moving the strip of filter material over the base after a quantity of drink has been brewed and has been removed via the piece of filter material. The means for moving the strip of filter material comprise a separate transport unit (14), and fixing means (28,29) are provided for fixing the transport unit to one of two opposing sides of the base, as desired. The means for moving the strip of filter material can also comprise a separate guide unit (26), which is fixed in each case to that side of the base which is opposite to the side where the transport unit (14) is located. A supply unit (19) for filter material can also be fitted at the side of the base where the guide unit (26) is located. A winding unit (34) for used filter material is optionally fitted at the side of the base where the transport unit (14) is located.