The π-conjugated organic and polymeric semiconducting materials have attracted much attention in the past years due to their significant potential in applications to electronic and optoelectronic devices including organic field-effect transistors (OFETs), organic photovoltaics (OPVs), and organic light-emitting diodes (OLEDs), etc. Yet, organic and polymeric semiconductors still have challenges associated with their relatively low charge carrier (hole and electron) transport mobilities and ambient stability in OFET applications. This dissertation discusses the molecular engineering on backbones and side-chains of π-conjugated semiconducting polymers to enhance the hole and electron field-effect mobilities. Three donor-acceptor copolymers, the hole transport (p-type) poly(hexathiophene-co-benzo- thiazole) (PBT6), the hole transport poly(thiophenes-benzothiadiazole-thiophenes-diketopyrrolo- pyrrole) (pTBTD), and the electron transport (n-type) poly(dithieno-diketopyrrolopyrrole-bithiazole) (PDBTz) have been developed. Besides, the effect of polymer side chains on polymer solution-processability and charge carrier transport properties was systematically investigated: a side chain 5-decylheptadecyl having the branching position remote from the polymer backbone merges the advantages of the improved solubility from traditional branched side chains in which the branch chains are close to polymer backbone and the effective π-π intermolecular interactions commonly associated with linear side chains. This indicates the potential of side chain engineering to facilitate the charge carrier transport performance of organic and polymeric semiconductors. Additionally, PDBTz solution-processing to OFETs based on non-halogenated solvents (xylenes and tetralin) was studied. The resultant thin-film OFET devices based on non-halogenated solvents exhibited similar film morphology and field-effect electron mobilities as the counterparts based on halogenated solvents, indicative of the feasibility of developing high mobility OFET devices through more environmentally-benign processing.