A \lambda-configuration (v_k)_\lambda is a finite incidence structure of v points and v lines such that each line contains k points, through each point there are k lines, there are at most \lambda lines through two different points, and there are at most \lambda points in the intersection of two different lines. A 1-configuration is just called configuration (or maybe combinatorial configuration). A 2-configuration is also called spatial configuration. For \lambda > 2 we choose the name hyperspatial configuration. Modern research on spatial configurations started twenty years ago. Here first results for \lambda = 3 (and \lambda = 4) will be presented, i.e. existence, enumeration, special properties, infinite series etc.