Well-defined poly(L-lactide-b-2-dimethylaminoethyl methacrylate) (PLLA-b-PDMAEMA) linear AB block copolymers and BAB block copolymers with PLLA as the central block (PDMAEMA-b-PLLA-b-PDMAEMA) were synthesized by combined ring-opening polymerization and atom transfer radical polymerization. Molar masses of the PLLA block vary from 13K to 19K and the PDMAEMA block from 5K to 35K. Thermal properties, morphology, and crystallization kinetics of the copolymers were analyzed for crystallization conducted in the bulk, in thick and thin films, and in solution as well as for a limited number of stereocomplexes of diblock and triblock copolymers with poly(D-lactide) in thin films and of partially quaternized diblock copolymers. In the bulk, it is shown that crystallization rates are reduced and morphologies disordered when adding a PDMAEMA block to PLLA; these tendencies are more pronounced in the triblock compared to diblock copolymers of the same PDMAEMA content. Usually, G, the local growth rate, and K, the overall growth rate, vary in the same direction (with temperature or PDMAEMA content): the addition of a PDMAEMA block decreases both G and K more or less similarly. However, an inverse effect is seen upon quaternization: G decreases (slightly) as expected, due to the decreased mobility of the molecules, but K still increases due to the formation of a larger number of nuclei in the system. This antagonist effect between G and K is also seen, to a smaller extent, when comparing diblock and triblock copolymers. For the same PDMAEMA content, G is smaller in the triblock polymer while K remains almost constant, again compensating the decrease of G, by the creation of more nuclei. In terms of morphology, crystallization in thin films (30 nm) and in solution leads to single crystals that are more disordered (or distorted) for the triblock copolymers than for the diblock copolymers. The addition of PDLA homopolymer also leads to single crystals in thin films with the diblock as well as the triblock copolymers. If the enantiomeric compositions lead to hexagonal-shape crystals in blends with diblock copolymers, whereas nonenantiomeric compositions give triangular-shape crystals, the stereocomplexes involving triblock copolymers also give triangular-shape crystals even at enantiomeric compositions; an excess of copolymer is needed to regenerate the hexagonal single crystals.