Pore space microstructure transitions in porous media are investigated by means of simulations of pore networks subject to a random compaction mechanism. With critical path analysis we track the characteristic pore length of the media. This pore length becomes singular at transition porosities, exhibiting kinks and even discontinuities if compaction is strong. The transitions arise from the appearance of new modes in the pore size distribution. Different modes control the transport properties in different porosity intervals where the characteristic pore length is continuous. These continuous pieces of pore length correspond to structurally different media. A transition occurs when the pore fraction controlling flow equals the critical percolation probability of the underlying lattice representing the pore space. To prove the validity of the transitions discovered by simulation we develop an analytical description of the pore-size distribution of media under compaction by using a detailed balance of pore populations. Analytical transition porosities agree precisely with simulations. At the first pore space microstructure transition the change in characteristic length l (P) exhibits a critical scaling Delta l (P) alpha (lambda(c) - lambda) (upsilon) , with upsilon = 1 and lambda a compaction factor. Within this approach many aspects of the pore space microstructure transitions observed in the simulations are explained.