The structural and functional effects of fine-textured matrices with sub-micron features on the growth of cardiac myocytes were examined. Electrospinning was used to fabricate biodegradable non-woven poly(lactide)- and poly(glycolide)-based (PLGA) scaffolds for cardiac tissue engineering applications. Post-processing was applied to achieve macro-scale fiber orientation (anisotropy). In vitro studies confirmed a dose-response effect of the poly(glycolide) concentration on the degradation rate and the pH value changes. Different formulations were examined to assess scaffold effects on cell attachment, structure and function. Primary cardiomyocytes (CMs) were cultured on the electrospun scaffolds to form tissue-like constructs. Scanning electron microscopy (SEM) revealed that the fine fiber architecture of the non-woven matrix allowed the cardiomyocytes to make extensive use of provided external cues for isotropic or anisotropic growth, and to some extent to crawl inside and pull on fibers. Structural analysis by confocal microscopy indicated that cardiomyocytes had a preference for relatively hydrophobic surfaces. CMs on electrospun poly(L-lactide) (PLLA) scaffolds developed mature contractile machinery (sarcomeres). Functionality (excitability) of the engineered constructs was confirmed by optical imaging of electrical activity using voltage-sensitive dyes. We conclude that engineered cardiac tissue structure and function can be modulated by the chemistry and geometry of the provided nano- and micro-textured surfaces. Electrospinning is a versatile manufacturing technique for design of biomaterials with potentially reorganizable architecture for cell and tissue growth.