## 1 Introduction  
In a seminal result in 1984, [PERSON] and [PERSON] showed that it is possible for two parties to distribute a secret key in a way that is unconditionally secure against any adversary, even a quantum one [1]. This fundamental primitive, namely quantum key distribution (QKD), is of great importance for many cryptographic tasks, such as one-time pad encrypted secure communication [2] or message authentication [3]. It has been thoroughly studied both in theory and in practice; indeed, the rapid progress in the field has enabled the distribution of secret keys with information-theoretic security over deployed optical fiber networks [4, 5], and QKD systems are available on the market [6]. The two communicating parties of a QKD protocol [7], [PERSON] and [PERSON], can in principle share an information-theoretic secret key after the exchange of a large number of quantum signals through a physical channel, known as a quantum channel, which is subject to eavesdropping, and additional information sent on a public, but authenticated classical channel. After [PERSON] and [PERSON] have agreed on a set of non-commuting quantum operators, they can encode some information into these variables: any attempt by the eavesdropper, [PERSON], to recover this information necessarily disturbs the transmitted quantum states and is discovered after random sampling of a fraction of [PERSON] and [PERSON]'s correlated data. In most commonly-used QKD systems, the key information is encoded on properties of single photons, and thus, specific components for single-photon detection are required. The quest for high-performance quantum key distribution systems in the last few years has led to several successful demonstrations based on these discrete-variable or distributed-phase reference protocols [8, 9, 10, 11]. There exists, however, a different type of protocol, in which information is carried by properties of light that are continuous, such as the values of the quadrature components of a coherent state. The use of such continuous-variable quantum information carriers, instead of qubits, constitutes a powerful alternative approach for QKD and more generally for quantum information processing [12]. From a practical point of view, for instance, continuous-variable (CV) QKD protocols present the major advantage that they only require standard telecommunication technology, and in particular, instead of dedicated photon-counting technology, they use coherent detection techniques widely used in classical optical communications. It is important to emphasize that there is a significant conceptual difference between these protocols and the standard BB84 protocol proposed by [PERSON] and [PERSON] [1] and other discrete-variable protocols, even if the latter use coherent states: as we will see in detail in the following sections, information is encoded on non-orthogonal states, which captures the quantum nature of the CVQKD protocols; however, entirely different degrees of freedom are used in this case. This brings the need for different security proof techniques while at the same time opening the way to very practical implementations. In the following, we begin by describing, in Section 2, the principle of CVQKD protocols focusing in particular on protocols using Gaussian modulation of coherent states. We then proceed in Section 3 with an overview of the current status of security proofs for such protocols. In Section 4, we discuss the implementations of CVQKD protocols, including the first long-distance experiments of quantum key distribution using continuous variables, and in Section 5, we provide a brief overview of theoretical and experimental studies on the security of CVQKD systems in the presence of practical imperfections and side channels. Finally, in Section 6, we provide a comprehensive presentation of major challenges andperspectives in the field.