Isolating single molecules in the solid state has allowed fundamental experiments in basic and applied sciences. When cooled down to liquid helium temperature, certain molecules show transition lines, that are tens of megahertz wide, limited only by the excited state lifetime. The extreme flexibility in the synthesis of organic materials provides, at low costs, a wide palette of emission wavelengths and supporting matrices for such single chromophores. In the last decades, the controlled coupling to photonic structures has led to an optimized interaction efficiency with light. Molecules can hence be operated as single photon sources and as non-linear elements with competitive performance in terms of coherence, scalability and compatibility with diverse integrated platforms. Moreover, they can be used as transducers for the optical read-out of fields and material properties, with the promise of single-quanta resolution in the sensing of charges and motion. We show that quantum emitters based on single molecules hold promise to play a key role in the development of quantum science and technologies. Modern societies have an ever-growing need for efficient computation techniques and for fast and secure communication, to distribute a huge amount of data around the globe. By harnessing quantum effects present at the nanoscale, new quantum technologies can be employed to meet these needs, including quantum cryptography and fully-fledged quantum information processing. On the other hand, the extreme sensitivity of quantum systems to their local environment can be exploited to also create new sensing devices, which provide unprecedented precision, accuracy and resolution and can be deployed within large quantum networks. Key applications require the generation and manipulation of quantum states of light, such as photonic quantum simulation [1, 2], linear optical quantum computing [3], device-independent or long-distance quantum key distribution protocols [4], sub-shot-noise imaging [5] and quantum metrology [6, 7]. In this context, single impurities in solid-state systems can act as bright, on-demand single-photon sources (SPSs), which are a crucial resource in these photonic quantum technologies. Quantum emitters may also perform as non-linear elements at the few-photon level [8] and as nanoscale sensors, allowing the optical read-out of local properties of materials and fields. In this context, single molecules in the solid-state offer competitive and reliable properties, with several key advantages. First, they are very small and have well-defined transition dipole moments so that they can be used as nanoscopic sensors for a number of scalar and vector quantities such as pressure, strain, temperature, electric and magnetic fields, as well as optical fields. Second, organic molecules can be designed and synthesized for different parts of the visible spectrum and integrated in a range of organic matrices, a feature that is a severe limiting factor for color centers in diamond or lithographically produced semiconductor quantum dots. Third, the combination of small size and ease of fabrication makes organic molecules ideal for applications where high densities and scalability are desirable. Fourth, organic dye molecules can have strong zero-phonon lines, which reach their Fourier-limited natural linewidth at liquid helium temperature, thus providing very bright and stable sources of photons with a high degree of coherence. Although many of these features have been known since the early nineties, thanks to the development of specific, efficient light-molecule interfaces and hybrid molecular devices in the last ten years, molecular quantum emitters are making the jump from proof-of-principle to the era of complex quantum optics experiments and multi-photon devices. Here we review the recent advances of single-molecule studies for quantum technologies, with a special focus on the coupling to nanophotonic structures for the enhancement and control of their interaction with quantum light. We discuss how this can extend the quantum optical toolbox for molecules, enabling flexible and efficient quantum photonic devices and new diverse applications. In Section 1 we discuss some fundamentals of molecules and their photophysics. For a general overview in the field of single-molecule physics and spectroscopy, we refer the reader to review papers such as Refs. [9,10,11]. Some key experiments of the past decade are then summarized, with single molecules acting as well-isolated single quantum