Spatially-resolved studies of nearby star-forming galaxies are essential to understand various physical and chemical phenomena at play in the interstellar medium in the galaxies, and consequently to obtain a comprehensive picture of galaxy formation and evolution. In this thesis, I perform spatially-resolved analyses of chemical abundances and star-formation in nearby star-forming galaxies - blue compact dwarf galaxies (BCDs) and spiral galaxies. I map various properties of H II regions and the surrounding gas within three BCDs, using integral field spectroscopic (IFS) data from the Gemini Multi-Object Spectrograph-North. While answering questions related to chemical homogeneity, ionisation mechanisms and stellar populations within BCDs, I address more profound issues, which go beyond the characterisation of studied BCDs and aim to explain global phenomena with broader implications. The BCD NGC 4449 hosts a metal-poor central star-forming region, which I explain by various scenarios related to the interplay between star-formation, metal-distribution and gas dynamics within galaxies. The BCD NGC 4670 shows an unusual negative relationship between the nitrogen-to-oxygen ratio and oxygen abundance at spatially-resolved scales. I explore this relation with chemical evolution models and by comparison to other star-forming galaxies and suggest that nitrogen enrichment, variations in star-formation efficiency or hydrodynamical effects may be responsible for the observed relation. For another BCD, SBS 1415+437, the spatially-resolved abundances on average agree with the integrated abundance, implying that low-redshift spatially-resolved results may be directly compared with unresolved high-redshift results. I study spiral galaxies to address long-standing issues related to the reliability of metallicity calibrators and the Schmidt Law of star-formation. Using IFS data of twenty-four spiral galaxies taken with the Multi-Unit Spectroscopic Explorer, I find that the current strong-line metallicity calibrators for H II regions are unsuitable for regions dominated by diffuse ionised gas (DIG). I devise new recipes for estimating the metal-content of the DIG. For another set of nine spiral galaxies, I use multi-wavelength data to show that the spatially-resolved Schmidt relation is very sensitive to the consideration of diffuse background, which is a component unrelated to the current star-formation. Removal of this component from the SFR tracers and the atomic gas results in similar local and global Schmidt relation. To conclude, the spatially-resolved analyses presented in this thesis have led to discoveries and further questions, which I will address in my ongoing and future works.