A system, comprising: a refill container comprising a body defining a cavity storing a composition; and a pump dispenser, comprising: a container (2; 3) comprising a body defining a chamber for storing a product and defining an opening at a first end of the chamber through which the product is dispensable from the chamber and through which the refill container is insertable into the chamber, the body having a first surface at a second end of the chamber, opposite from the first end of the chamber; a closure movable relative to the body between a closed position at which the closure blocks the opening and an open position at which the opening is not blocked by the closure; a pump for pumping the product from the chamber; and a projection extending from the closure, the projection comprising a first portion extending from the closure in a first direction and a second portion extending from the first portion in a second direction, the second direction being different to the first direction, the second portion having a second surface that faces and approaches the first surface of the body when the closure is moved relative to the body from the open position to the closed position and that is adapted to cooperate with the first surface of the body to compress or squeeze the refill container inserted into the chamber therebetween, wherein the first portion of the projection comprises a dip tube with a lumen fluidly connected to the pump. a refill container comprising a body defining a cavity storing a composition; and a pump dispenser, comprising: a container (2; 3) comprising a body defining a chamber for storing a product and defining an opening at a first end of the chamber through which the product is dispensable from the chamber and through which the refill container is insertable into the chamber, the body having a first surface at a second end of the chamber, opposite from the first end of the chamber; a closure movable relative to the body between a closed position at which the closure blocks the opening and an open position at which the opening is not blocked by the closure; a container (2; 3) comprising a body defining a chamber for storing a product and defining an opening at a first end of the chamber through which the product is dispensable from the chamber and through which the refill container is insertable into the chamber, the body having a first surface at a second end of the chamber, opposite from the first end of the chamber; a closure movable relative to the body between a closed position at which the closure blocks the opening and an open position at which the opening is not blocked by the closure; a pump for pumping the product from the chamber; and a projection extending from the closure, the projection comprising a first portion extending from the closure in a first direction and a second portion extending from the first portion in a second direction, the second direction being different to the first direction, the second portion having a second surface that faces and approaches the first surface of the body when the closure is moved relative to the body from the open position to the closed position and that is adapted to cooperate with the first surface of the body to compress or squeeze the refill container inserted into the chamber therebetween, wherein the first portion of the projection comprises a dip tube with a lumen fluidly connected to the pump.