Quantum memories matched to single photon sources will form an important cornerstone of future quantum network technology. We demonstrate such a memory in warm Rb vapor with on-demand storage and retrieval, based on electromagnetically induced transparency. With an acceptance bandwidth of δf ¼ 0.66 GHz, the memory is suitable for single photons emitted by semiconductor quantum dots. In this regime, vapor cell memories offer an excellent compromise between storage efficiency, storage time, noise level, and experimental complexity, and atomic collisions have negligible influence on the optical coherences. Operation of the memory is demonstrated using attenuated laser pulses on the single photon level. For a 50 ns storage time, we measure η 50 ns e2e ¼ 3.4ð3Þ% end-to-end efficiency of the fiber-coupled memory, with a total intrinsic efficiency η int ¼ 17ð3Þ%. Straightforward technological improvements can boost the end-to-end-efficiency to η e2e ≈ 35%; beyond that, increasing the optical depth and exploiting the Zeeman substructure of the atoms will allow such a memory to approach near unity efficiency. In the present memory, the unconditional read-out noise level of 9 × 10 −3 photons is dominated by atomic fluorescence, and for input pulses containing on average μ 1 ¼ 0.27ð4Þ photons, the signal to noise level would be unity. DOI: 10.1103/PhysRevLett.119.060502 Quantum networks built from optical fiber-linked quantum nodes [1] open manifold opportunities across a range of scientific and technological frontiers. For example, highspeed quantum cryptography networks can be used for unconditionally secure communication in metropolitan areas [2], and quantum networks can help realize large scale quantum computers and quantum simulators that will allow for exponential speed-up in solving complex problems [3,4]. Photonic quantum networks, in turn, require a scalable quantum node technology that allows for (i) storing quantum information in a quantum memory [5], and (ii) ondemand conversion of this information into single photons traveling along the network interconnects.To realize quantum nodes, a heterogeneous approach [6,7] is highly promising. Heterogeneous quantum nodes consist of a single photon source and a compatible quantum memory, where the systems may be completely different from each other and can be individually optimized. For the single photon source, self-assembled semiconductor quantum dots (QD) are arguably the best choice, as they allow for high speed on-demand photon generation with up to GHz emission rates and measured efficiencies [8-10] as high as 75%. These sources can emit indistinguishable single photons [9,11,12] or even polarization-entangled photon pairs [13,14], and the QD spin can be entangled with an emitted photon [15,16]. However, the quantum dot itself is not a good quantum memory, since the coherence times are limited by the comparably strong coupling to the solid-state environment. To make this exquisite source of single or entangled photons useful for quantum networks, the QD theref...