A negative pressure wound therapy (NPWT) bandage for applying negative pressure to a wound in skin of a patient, said NPWT bandage comprising: a membrane configured for disposition over a wound so as to form a wound chamber between said membrane and the wound, said membrane comprising a wound-side surface, an atmosphere-side surface, and an opening extending through said membrane from said wound-side surface to said atmosphere-side surface; and a pump assembly carried by said membrane, said pump assembly comprising: a pump body comprising a wall structure disposed about a pump chamber, wherein at least a portion of said wall structure is formed out of a resilient material such that at least a portion of said wall structure may be compressed inwardly by application of a force applied parallel to the skin of the patient; a wound-side passageway extending through said wall structure and communicating with the wound chamber through said opening formed in said membrane; a wound-side one-way valve disposed in said wound-side passageway, said wound-side one-way valve being configured to allow fluid to flow through said wound-side passageway from the wound chamber to said pump chamber but to prevent fluid from flowing through said wound-side passageway from said pump chamber to the wound chamber; an atmosphere-side passageway extending through said wall structure and connecting said pump chamber and the atmosphere; and an atmosphere-side one-way valve disposed in said atmosphere-side passageway, said atmosphere-side one-way valve being configured to allow fluid to flow through said atmosphere-side passageway from said pump chamber to the atmosphere but to prevent fluid from flowing through said atmosphere-side passageway from the atmosphere to said pump chamber; such that when a compressive force is applied to said wall structure of said pump body in a direction parallel to the skin of the patient, said wall structure is compressed inwardly and fluid within said pump chamber will be forced out of said pump chamber via said atmosphere-side passageway, and when the compressive force applied to said wall structure of said pump body is thereafter reduced, fluid within the wound chamber will be drawn into said pump chamber through said wound-side passageway, a membrane configured for disposition over a wound so as to form a wound chamber between said membrane and the wound, said membrane comprising a wound-side surface, an atmosphere-side surface, and an opening extending through said membrane from said wound-side surface to said atmosphere-side surface; and a pump assembly carried by said membrane, said pump assembly comprising: a pump body comprising a wall structure disposed about a pump chamber, wherein at least a portion of said wall structure is formed out of a resilient material such that at least a portion of said wall structure may be compressed inwardly by application of a force applied parallel to the skin of the patient; a wound-side passageway extending through said wall structure and communicating with the wound chamber through said opening formed in said membrane; a pump body comprising a wall structure disposed about a pump chamber, wherein at least a portion of said wall structure is formed out of a resilient material such that at least a portion of said wall structure may be compressed inwardly by application of a force applied parallel to the skin of the patient; a wound-side passageway extending through said wall structure and communicating with the wound chamber through said opening formed in said membrane; a wound-side one-way valve disposed in said wound-side passageway, said wound-side one-way valve being configured to allow fluid to flow through said wound-side passageway from the wound chamber to said pump chamber but to prevent fluid from flowing through said wound-side passageway from said pump chamber to the wound chamber; an atmosphere-side passageway extending through said wall structure and connecting said pump chamber and the atmosphere; and an atmosphere-side one-way valve disposed in said atmosphere-side passageway, said atmosphere-side one-way valve being configured to allow fluid to flow through said atmosphere-side passageway from said pump chamber to the atmosphere but to prevent fluid from flowing through said atmosphere-side passageway from the atmosphere to said pump chamber; an atmosphere-side passageway extending through said wall structure and connecting said pump chamber and the atmosphere; and an atmosphere-side one-way valve disposed in said atmosphere-side passageway, said atmosphere-side one-way valve being configured to allow fluid to flow through said atmosphere-side passageway from said pump chamber to the atmosphere but to prevent fluid from flowing through said atmosphere-side passageway from the atmosphere to said pump chamber; such that when a compressive force is applied to said wall structure of said pump body in a direction parallel to the skin of the patient, said wall structure is compressed inwardly and fluid within said pump chamber will be forced out of said pump chamber via said atmosphere-side passageway, and when the compressive force applied to said wall structure of said pump body is thereafter reduced, fluid within the wound chamber will be drawn into said pump chamber through said wound-side passageway,