A modular construction system that utilizes versatile construction components releasably attachable to one another, in virtually any desired direction, by use of one or more interconnect components positioned therebetween. Each construction component includes at least two inventive connective surfaces with a receiving region therein, while each interconnect component includes at least one coupling surface comprising multiple coupling elements capable of releasable frictional engagement with at least a portion of one or more receiving regions. The receiving regions, the interconnect components, and the coupling elements are sized and configured to (1) enable a first type of connection in which at least a portion of an interconnect component fits within and releasably connects overlapping connective surfaces of two construction components, and (2) optionally also enable a second type of connection, in which construction components are connected by an interconnect component that releasably engages with two or more proximal connective surfaces positioned and aligned in the same plane In one inventive embodiment, the receiving regions of the construction components are sized and configured to enable releasable coupling with male studs of conventional popular toy building blocks.