  Parallel transport in a fibre bundle with respect to smooth paths in the base
space B have recently been extended to representations of the smooth singular
simplicial set Sing_{smooth}(B).
  Inspired by these extensions,I revisit the development of a notion of
`parallel' transport in the topological setting of fibrations with the homotopy
lifting property and then extend it to representations of Sing(B) on such
fibrations. Closely related is the notion of (strong or `infty') homotopy
action, which has variants under a variety of names.
