Humankind will detect the first gravitational wave (GW) signals from the Universe in the current decade using ground-based detectors. But the richest trove of astrophysical information lies at lower frequencies in the spectrum only accessible from space. Signals are expected from merging massive black holes throughout cosmic history, from compact stellar remnants orbiting central galactic engines from thousands of close contact binary systems in the Milky Way, and possibly from exotic sources, some not yet imagined. These signals carry essential information not available from electromagnetic observations, and which can be extracted with extraordinary accuracy. For 20 years, NASA, the European Space Agency (ESA), and an international research community have put considerable effort into developing concepts and technologies for a GW mission. Both the 2000 and 2010 decadal surveys endorsed the science and mission concept of the Laser Interferometer Space Antenna (LISA). A partnership of the two agencies defined and analyzed the concept for a decade. The agencies partnered on LISA Pathfinder (LPF), and ESA-led technology demonstration mission, now preparing for a 2015 launch. Extensive technology development has been carried out on the ground. Currently, the evolved Laser Interferometer Space Antenna (eLISA) concept, a LISA-like concept with only two measurement arms, is competing for ESA's L2 opportunity. NASA's Astrophysics Division seeks to be a junior partner if eLISA is selected. If eLISA is not selected, then a LISA-like mission will be a strong contender in the 2020 decadal survey. This Technology Development Roadmap (TDR) builds on the LISA concept development, the LPF technology development, and the U.S. and European ground-based technology development. The eLISA architecture and the architecture of the Mid-sized Space-based Gravitational-wave Observatory (SGO Mid)-a competitive design with three measurement arms from the recent design study for a NASA-led mission after 2020-both use the same technologies. Further, NASA participation in an ESA-led mission would likely augment the eLISA architecture with a third arm to become the SGO Mid architecture. For these reasons, this TDR for a future GW mission applies to both designs and both programmatic paths forward. It is adaptable to the different timelines and roles for an ESA-led or a NASA-led mission, and it is adaptable to available resources. Based on a mature understanding of the interaction between technology and risk, the authors of this TDR have chosen a set of objectives that are more expansive than is usual. The objectives for this roadmap are: (1) reduce technical and development risks and costs; (2) understand and, where possible, relieve system requirements and consequences; (3) increase technical insight into critical technologies; and (4) validate the design at the subsystem level. The emphasis on these objectives, particularly the latter two, is driven by outstanding programmatic decisions, namely whether a future GW mission is ESA-led or NASA-led, and availability of resources. The relative emphasis is best understood in the context of prioritization.