A programmable logic device has many regions of programmable logic, together with relatively general-purpose, programmable, interconnection resources that can be used to make interconnections between virtually any of the logic regions. In addition, various types of more local interconnection resources are associated with each logic region for facilitating the making of interconnections between adjacent or nearby logic regions without the need to use the general-purpose interconnection resources for those interconnections. The local interconnection resources support flexible clustering of logic regions via relatively direct and therefore high-speed interconnections, preferably in both horizontal and vertical directions in the typically two-dimensional array of logic regions. The logic region clustering options provided by the local interconnection resources are preferably boundary-less or substantially boundary-less within the array of logic regions.