  We show using bosonization methods that extended Hubbard-Heisenberg models on
two types of two leg ladders (without flux and with flux $\pi$ per plaquette)
have commensurate pair-density wave (PDW) phases. In the case of the
conventional (flux-less) ladder the PDW arises when certain filling fractions
for which commensurability conditions are met.
  For the flux $\pi$ ladder the PDW phase is generally present. The PDW phase
is characterized by a finite spin gap and a superconducting order parameter
with a finite (commensurate in this case) wave vector and power-law
superconducting correlations. In this phase the uniform superconducting order
parameter, the $2k_F$ charge-density-wave (CDW) order parameter and the
spin-density- wave N\'eel order parameter exhibit short range (exponentially
decaying) correlations. We discuss in detail the case in which the bonding band
of the ladder is half filled for which the PDW phase appears even at weak
coupling. The PDW phase is shown to be dual to a uniform superconducting (SC)
phase with quasi long range order. By making use of bosonization and the
renormalization group we determine the phase diagram of the spin-gapped regime
and study the quantum phase transition. The phase boundary between PDW and the
uniform SC ordered phases is found to be in the Ising universality class. We
generalize the analysis to the case of other commensurate fillings of the
bonding band, where we find higher order commensurate PDW states for which we
determine the form of the effective bosonized field theory and discuss the
phase diagram. We compare our results with recent findings in the
Kondo-Heisenberg chain. We show that the formation of PDW order in the ladder
embodies the notion of intertwined orders.
