A syringe assembly (10) includes a syringe barrel (12) having a proximal end and a distal end, a needle-bearing hub (20) coupled to the distal end of the syringe barrel (12). An adapter (32, 104, 120) is configured for connecting to a container containing a substance, such as a medication, drug, or pharmaceutical. The adapter has a body (54, 114, 148) with a cavity (76, 116, 160), a proximal end, and a distal end. A closure member (84, 105) is coupled to the proximal end of the body. The closure member has a thickness where a needle of a syringe can pierce the closure member to access the cavity of the body. A cannula (98, 118, 170) extends from the distal end of the body for accessing the container.