Kimberlite pipes or dykes tend to occur in clusters (a few kilometres in diameter) within fields ∼30-50 km in diameter. They are generally considered to originate from low degrees of partial melting of carbonated peridotite within zones of ascending mantle. Numerical modelling shows that at the depth of formation of kimberlite melts (≫200 km), mantle compaction processes can result in the formation of melt pockets a few tens of kilometres across, with melt concentrations up to 7%. The initiation of swarms of kimberlite dykes at the top of these melt pockets is inevitable because of the large excess pressure between the melt and the surrounding solid, which exceeds the hydraulic fracturing limit of the overlying rocks. After their initiation at mantle depth the swarm of dykes may reach the surface of the Earth when the entire cratonic lithosphere column is in extension. We propose that kimberlite fields represent the surface envelope of dyke swarms generated inside a melt pocket and that kimberlite clusters represent the discharge of melt via dykes originating from sub-regions of the pocket. This model reproduces the worldwide average diameter of kimberlite fields and is consistent with the observation that some of the main kimberlite fields display age ranges of c. 10 Myr. It is deduced that, at the scale of the Kaapvaal craton, different fields such as Kimberley, N. Lesotho and Orapa, dated at 80-90 Ma, probably result from synchronous melt pockets forming inside an ascending mantle flow. The same model could apply to the fields of the Rietfontein, Central Cape and Gibeon districts dated at 60-70 Ma. It is suggested that the same mantle flow that produced the Kimberley, N. Lesotho and Orapa fields migrated over ∼20-30 Myr a few hundred kilometres westward to form the Rietfontein, Central Cape and Gibeon fields.