## 1 Introduction  
Passively mode-locked fibre lasers generate ultrashort pulses with high peak power and broad optical spectrum, which have attracted growing attention in the past decades due to the advantages of compactness, stability, easy handling and portability [1; 2]. The great potential has enabled a wealth of applications in military, industry, fundamental science, biomedicine, etc. In most cases, one single pulse travels through the entire round trip, with a repetition rate inversely proportional to the optical length of the laser cavity. However, higher pumping can lead to pulse splitting and coexistence of several pulses inside the cavity because a fibre laser can only withstand a certain amount of nonlinear phase shift. Depending on a comprehensive interaction via nonlinearity, dispersion, gain, loss, etc. inside the cavity, a fibre laser serves as a complex dissipative system and a versatile platform for plentiful pulse states such as harmonic mode-locking, pulse bunching and soliton molecules [3]. In particular, recent advances on saturable absorbers and dispersion schemes are of important benefit to control the experimental parameters and therefore enable observation of various states of soliton molecules. In analogy to molecules in chemistry which achieve balance of atoms via strong chemical bond, soliton molecules as a boundary soliton state are comprised of several individual pulses and result from balance of repulsive and attraction forces between solitons caused by many effects including nonlinear [for instance, cross phase modulation (XPM), gain saturation, saturable absorption, etc.] and dispersive effects [4]. Such a balance causes that several identical pulses (exactly the same intensity, as well as the same spectral and temporal profiles) travel through the cavity and keep a constant temporal separation and a fixed phase difference between neighbouring pulses. Although solitons pairs exhibiting variant characteristic parameters such as evolving phase [5] are sometimes referred to soliton molecules too, we focus on \"soliton molecules\" in this Review as stationary soliton pairs preserving all details for at least thousands of round trips in a cavity. Such soliton molecules are of vital significance to understand and explore. The reason is twofold: on the one hand, they are the most frequently observed in fibre lasers as an outcome of the complex nonlinear dynamics, which help us to retrieve the underlying dissipation nature; on the other hand, they are particularly useful for developing larger telecommunication capacity in optical fibre transmission lines [6; 7; 8] and advancing ultrafast characterization approaches such as real-time spectroscopy [9; 10]. Soliton molecules were first predicted theoretically by [PERSON] within the framework of nonlinear Schrodinger-Ginzburg-Landau equation [11] and coupled nonlinear Schrodinger equations [12]. [PERSON] et al. and [PERSON] et al. also investigated analytically and numerically the existence and stability of bound states with \(\pi\), 0 and \(\pm\pi/2\) phase differences [13; 14; 15]. So far bound states have been studied by simulated and/or experimental methods in types of fibre laser cavities, i.e., in soliton [16; 17], stretched-pulse [18], gain-guided [19] and self-similar [20] regimes, as well as dissipative soliton regime associating with large net-normal dispersion and spectral filtering [21]. A lot of experimental observations of bound solitons have been reported in fibre lasers mode-locked by nonlinear polarization evolution (NPE) [22; 23; 24], nonlinear amplifying loop mirror (NALM) [8; 25] and some real saturable absorbers (e.g., semiconductor saturable absorber mirror (SESAM) [26], carbon nanotubes (CNT) [27; 28; 29], graphene [30; 31], topological insulator [32], molybdenum disulphide (MoS\({}_{2}\)) [33] and black phosphorus [34]).