Nature employs lipid structures as a smart, environment-sensitive packaging material that also acts as a two dimensional solvent for proteins, receptors and channels to interact at the interface between these compartments. Even simple vesicles reconstituted in vitro with minimal lipid components can exhibit a zoology of morphological changes, phase behavior and biomimetic properties, for instance budding and fusion. These attributes make liposomes a desirable material for engineering soft, functional containers for confinement and transport of chemicals in novel technologies such as microfluidic platforms or targeted delivery systems. Another bioinspired strategy with technological promise is the programmable assembly of nanoscale and microscale components by the binding of complementary DNA sequences. The digitally-encoded recognition between oligomeric, single DNA strands is highly sensitive to single base mismatches and environmental conditions, affording the potential of fine control over self-assembling structures. Single stranded DNA modified with a hydrophobic group anchors the oligonucleotide to the outer monolayer of fluid vesicle membranes. We demonstrate the assembly of large (100nm) and giant (>5µm) vesicles decorated with complementary DNA sequences. Three regimes of aggregation behavior are observed: no aggregation, stable aggregates and aggregates that grow continually with time. The aggregate size and growth kinetics can be controlled by choice of system parameters, for example the number of DNA per vesicle, the ionic strength of the solution and the electrical potential of the vesicle membrane. The vesicle structures that form are reversible: repeatedly heating and cooling through the DNA melting transition unbinds and rebinds the vesicle assemblies. The melting temperature of DNA is sensitive to the lipid composition of the vesicles. This can be understood by modeling how the inter-membrane repulsive pressure tilts the free energy landscape of the DNA. Phase separation in the membrane can be utilized to confine the DNA to localized regions on the vesicle surface. We find that the partitioning of the DNA between lipid phases is sensitive to the anchoring technique that is employed. These results illustrate that careful engineering of the lipid composition as well as the attached nucleic acid sequences is a valuable tool in controlling the self-assembly of hierarchical superstructures of DNA-tethered vesicles.