Concentrations of dykes of basic composition emplaced in the same igneous episode or along similar trends are known as mafic dyke swarms and they occur in a wide variety of environments and over a wide range of scales on Earth. Recent radar mapping of Venus has revealed families of linear features interpreted to be the surface expression of near-surface dyke swarms. The lack of significant erosion on Venus provides a view of the surface manifestation of dyke swarm emplacement, one which complements the terrestrial perspective of erosion to deeper levels. The goal of this review is to synthesize the information available on both planets in order to use the complementary and synergistic record of mafic dyke swarm emplacement to build toward a better understanding of this important phenomenon in planetary history. We focus on the formation and evolution of giant dyke swarms which cover tens to hundreds of thousands of square kilometres on both Earth and Venus. Mafic dyke swarms on Earth occur in a wide range of modes and are observed in environments ranging from volcanic edifices (e.g., Hawaii), to central complexes (e.g., Spanish Peaks Complex, USA; Ramon Swarm, Israel), spreading centres and ophiolite complexes, compressional plate boundaries in back-arc settings (Columbia River Basalts, USA) and in continent-continent collisions. One of the most impressive modes of occurrence is that linked to the formation and evolution of mantle plumes. Terrestrial examples include a giant radiating swarm covering 100° of azimuth (the Mackenzie swarm, Canada), a 360° giant radiating swarm (the Central Atlantic reconstructed swarm), deformed giant radiating swarms (the Matachewan swarm, Canada), rift-arm associated swarms (e.g., Grenville swarm, Canada; Yakutsk swarm, Siberia), and one consisting of widely separated dykes (e.g., the Abitibi swarm, Canada). We summarize the geometric, chemical and isotopic characteristics of terrestrial dyke swarms, including their size and geometry, ages, presence and absence of subswarms, and the relation between swarms of different ages. We also summarize the characteristics of individual dykes, examining dyke length and continuity, en echelon offsets, dyke bifurcation, dyke height, width and depth, dyke intrusion and cooling history, and evidence for flow directions. On Venus at least 163 large radiating lineament systems (radius generally > 100 km) composed of graben, fissure and fracture elements have been identified. On the basis of their structure, plan view geometry and volcanic associations, the radial elements of more than 70% of these are interpreted to have formed primarily through subsurface dyke swarm emplacement, with the remainder forming through uplift or some combination of these two mechanisms. These systems are essentially uneroded and provide a view of the surface characteristics of giant radial swarms prior to the erosion which commonly occurs on Earth. The individual graben, fissures and fractures of which the systems are composed are typically less than several kilometres in width and cluster near the centre, with fissures grading smoothly into fractures at greater distances to define the overall radial pattern. While the largest systems, like those on Earth, are thousands of kilometres in radius, the population average is about 325 km, and they generally do not extend to equal lengths in all directions. In their distal regions, however, the elements in 72% of the systems continue along a purely radial trend, while distal elements in the remaining 28% curve gradually into unidirectional, sub-parallel geometries, generally interpreted to be related to regional stress patterns. The radial systems have a strong association with volcanism; all but seven display some form of volcanic signature. A review of models of the emplacement of lateral dykes from magma chambers under constant (buffered) driving pressure conditions and declining (unbuffered) driving pressure conditions indicates that the two pressure scenarios lead to distinctly different styles of dyke emplacement. Emplacement of lateral dykes in the constant driving pressure (buffered) case, however, can produce dykes which have sizes and widths which are very large and independent of chamber size. On Earth, the characteristics of giant mafic dyke swarms such as the Mackenzie dyke swarm in Canada strongly suggest that they were emplaced in buffered conditions. On Earth, giant radiating dyke swarms are usually preserved as fan-shaped fragments which have been dismembered and distorted by subsequent plate tectonic rifting events. The abundant intact giant radiating swarms on Venus provide criteria by which fragmented terrestrial swarms can be reconstructed.