A system for making beverages, comprising at least one extraction device and a capsule for making beverages, wherein the capsule comprises: - a cup-shaped containment body which inside it forms a chamber, the containment body comprising a bottom portion and a lateral wall, the lateral wall being connected to the bottom portion and forming an access opening for accessing the chamber; - a powdered food substance, contained in the capsule and housed in the chamber, the powdered food substance allowing a beverage to be made by passing hot water through it; - a closing element fixed to the lateral wall at the access opening for closing it; - a filter element which is permeable to water and is positioned inside the chamber between the powdered food substance and the bottom portion; characterized in that the extraction device comprises: - a first part comprising a housing for the capsule, and a second part, the first part and the second part being mobile one relative to the other between an operating position in which they clamp between them a capsule inserted in the housing, and a home position in which they allow the insertion and removal of the capsule respectively in and from the housing; - one or more piercing elements associated with the housing for piercing the bottom portion of the capsule inserted in the housing at least when the first part and the second part are in the operating position; - piercing means designed to pierce the closing element of the capsule at least when the capsule is inserted in the housing, the first part and the second part are in the operating position and the pressure in the chamber exceeds a predetermined value; and in that the extraction device comprises water feeding means operatively associated with the housing for in use supplying water into the capsule through the bottom portion pierced by the one or more piercing elements, the bottom portion of the capsule constituting, in use, an infeed section for feeding hot water into the capsule and the closing element of the capsule constituting, in use, an outfeed section through which the beverage can come out of the chamber; in that the filter element of the capsule rests on the bottom portion and is free to move away from the latter towards the inside of the chamber, except for the resistance applied by the powdered food substance, in such a way that the filter element is movable between a first position, in which the filter element rests on the bottom portion, and a second position, in which the filter element is spaced apart from said bottom portion; and in that, when the capsule is inserted in the housing and the first part and the second part are in the operating position, the one or more piercing elements hold the filter element in the second position in which the filter element is spaced apart from the bottom portion. - a cup-shaped containment body which inside it forms a chamber, the containment body comprising a bottom portion and a lateral wall, the lateral wall being connected to the bottom portion and forming an access opening for accessing the chamber; - a powdered food substance, contained in the capsule and housed in the chamber, the powdered food substance allowing a beverage to be made by passing hot water through it; - a closing element fixed to the lateral wall at the access opening for closing it; - a filter element which is permeable to water and is positioned inside the chamber between the powdered food substance and the bottom portion; - a first part comprising a housing for the capsule, and a second part, the first part and the second part being mobile one relative to the other between an operating position in which they clamp between them a capsule inserted in the housing, and a home position in which they allow the insertion and removal of the capsule respectively in and from the housing; - one or more piercing elements associated with the housing for piercing the bottom portion of the capsule inserted in the housing at least when the first part and the second part are in the operating position; - piercing means designed to pierce the closing element of the capsule at least when the capsule is inserted in the housing, the first part and the second part are in the operating position and the pressure in the chamber exceeds a predetermined value;