This critical review discusses the current understanding of droplet formation, transport, and merging in microfluidics. The authors focus on the physical ingredients that determine the flow of droplets in microchannels and recall classical results of fluid dynamics to explain observed behaviors. They introduce the main physical ingredients that differentiate droplet microfluidics from single-phase microfluidics, such as the modifications to the flow and pressure fields introduced by interfacial tension. The review covers three practical aspects: (i) The formation of droplets and the dominant interactions depending on the geometry in which they are formed, (ii) The transport of droplets, including the evaluation of drop velocity, pressure-velocity relationships, and the flow field induced by the presence of the droplet, and (iii) The fusion of two droplets, including different methods of bridging the liquid film between them. The introduction highlights the motivations for manipulating droplets in microchannels, including their use in material science applications and lab-on-a-chip devices. The review also discusses the advantages and challenges of using droplets in microfluidics, such as control over dispersion and mixing of chemicals and the simplification of manipulation of small volumes. The physical ingredients that differentiate droplet microfluidics from single-phase microfluidics are discussed, focusing on the role of interfacial tension. This includes the forces and energy associated with interfacial tension and the resulting pressure variations within droplets. Dimensionless numbers, such as the Weber number, Capillary number, and Bond number, are introduced to describe the relative importance of different physical effects. The review then delves into the production of droplets in microchannels, covering three main approaches: breakup in co-flowing streams, breakup in cross-flowing streams, and breakup in elongational strained flows. Each approach is analyzed in detail, including the mechanisms behind droplet formation and the influence of various parameters such as viscosity ratios, channel geometry, and flow rates. The transport of droplets in microchannels is discussed, focusing on bubbly flows and slug flows. The presence of lubrication films and their impact on droplet velocity is explained, along with the pressure drop vs. droplet velocity relationships and the flow patterns induced by the immiscible interface. Finally, the review explores the flow fields and mixing effects induced by the presence of droplets. It discusses the creation of recirculation zones and stagnation points, the enhancement of mixing, and the effects of surfactant molecules on the interface.This critical review discusses the current understanding of droplet formation, transport, and merging in microfluidics. The authors focus on the physical ingredients that determine the flow of droplets in microchannels and recall classical results of fluid dynamics to explain observed behaviors. They introduce the main physical ingredients that differentiate droplet microfluidics from single-phase microfluidics, such as the modifications to the flow and pressure fields introduced by interfacial tension. The review covers three practical aspects: (i) The formation of droplets and the dominant interactions depending on the geometry in which they are formed, (ii) The transport of droplets, including the evaluation of drop velocity, pressure-velocity relationships, and the flow field induced by the presence of the droplet, and (iii) The fusion of two droplets, including different methods of bridging the liquid film between them. The introduction highlights the motivations for manipulating droplets in microchannels, including their use in material science applications and lab-on-a-chip devices. The review also discusses the advantages and challenges of using droplets in microfluidics, such as control over dispersion and mixing of chemicals and the simplification of manipulation of small volumes. The physical ingredients that differentiate droplet microfluidics from single-phase microfluidics are discussed, focusing on the role of interfacial tension. This includes the forces and energy associated with interfacial tension and the resulting pressure variations within droplets. Dimensionless numbers, such as the Weber number, Capillary number, and Bond number, are introduced to describe the relative importance of different physical effects. The review then delves into the production of droplets in microchannels, covering three main approaches: breakup in co-flowing streams, breakup in cross-flowing streams, and breakup in elongational strained flows. Each approach is analyzed in detail, including the mechanisms behind droplet formation and the influence of various parameters such as viscosity ratios, channel geometry, and flow rates. The transport of droplets in microchannels is discussed, focusing on bubbly flows and slug flows. The presence of lubrication films and their impact on droplet velocity is explained, along with the pressure drop vs. droplet velocity relationships and the flow patterns induced by the immiscible interface. Finally, the review explores the flow fields and mixing effects induced by the presence of droplets. It discusses the creation of recirculation zones and stagnation points, the enhancement of mixing, and the effects of surfactant molecules on the interface.