The demonstration, during the course of this doctoral project, of an effectively single-mode hollow-core anti-resonant optical fibre with loss rivalling that of single-mode silica fibre represents a huge milestone in the development of hollow-core fibre technology that has the potential to transform the field of fibre optics and its many applications. As attention increasingly turns to a focus on deploying hollow-core fibre in real world applications, one largely unexplored topic is that of multi-mode hollow-core anti-resonant optical fibres. Unlike in solid-core fibre where multiple modes can be guided with virtually the same attenuation, multi-mode guidance in hollow-core fibres presents a unique challenge in the form of large differential loss – and in general optical properties – between modes. Nevertheless, multi-mode guidance in a hollow core presents opportunities in many application areas, including high-power laser delivery, short-haul telecommunication systems and light-gas interaction systems, whilst offering lower loss, nonlinearity and latency across larger bandwidths than solid-core fibres. This thesis presents research concerning the nature of multi-mode guidance in anti-resonant optical fibres, their characteristics and their design for practical applications. Numerical simulation is applied extensively to study in detail the origins of the differential modal properties of these fibres, including attenuation and dispersion, leading to a new understanding of the processes involved. This facilitated the development of methods to engineer the differential properties of the anti-resonant fibres in order to achieve multi-mode guidance in fibres with a variety of micro-structure designs. Methods based on structural design and deployment conditions are explored. Design techniques are presented for multi-mode anti-resonant fibres targeting specific requirements in several application areas: short-haul telecommunications, delivery of high-power laser light and finally, fibre based gas sensors.