Within the currently well-established ΛCDM cosmological framework we still lack a satisfactory un- derstanding of the processes that trigger, regulate and eventually quench star formation on galactic scales. Gas flows (including inflows from the cosmic web and supernovae-driven outflows) are con- sidered to act as self-regulatory mechanisms, generating the scaling relations between stellar mass, star formation rate and metallicity observed in the local Universe by large spectroscopic surveys. These surveys, however, have so far been limited by the availability of only one spectrum per galaxy. The aim of this dissertation is to expand the study of star formation and chemical abundances to resolved scales within galaxies by using integral field spectroscopy (IFS) data, mostly from the ongoing SDSS- IV MaNGA survey. In the first part of this thesis I demonstrate the ubiquitous presence of extended low ionisation emission-line regions (LIERs) in both late- and early-type galaxies. By studying the Hα equivalent width and diagnostic line ratios radial profiles, together with tracers of the underlying stellar popula- tion, I show that LIERs are not due to a central point source but to hot evolved (post-asymptotic giant branch) stars. In light of this, I suggest a new classification scheme for galaxies based on their line emission. By analysing the colours, star formation rates, morphologies, gas and stellar kinematics and environmental properties of galaxies with substantial LIER emission, I identify two distinct popula- tions. Galaxies where the central regions are LIER-like, but show star formation at larger radii are late types in which star formation is slowly quenched inside-out. This transformation is associated with massive bulges. Galaxies dominated by LIER emission at all radii, on the other hand, are red-sequence galaxies harbouring a residual cold gas component, acquired mostly via external accretion. Quiescent galaxies devoid of line emission reside in denser environments, which suggests environmental effects as a likely cause for the existence of line-less galaxies on the red sequence. In the second part of this dissertation I focus on the study of resolved chemical abundances by characterising the gas phase oxygen and nitrogen abundance gradients in a large sample of star forming galaxies. I analyse the deviations from an exponential profile at small and large radii and the dependence of the gradients on stellar mass. These findings are interpreted in the context of the inside-out paradigm of disc growth. I then demonstrate the necessity of gas flows, which are responsible for the observed flattening of the metallicity and N/O ratio gradients at large radii. Finally, I present a case study based on one nearby galaxy (NGC 628), in which I combine IFS and cold gas data to derive a spatially resolved metal budget and estimate the mass of metals lost by the galaxy throughout its life- time. By using simple physically-motivated models of chemical evolution I infer the average outflow loading factor to be of order unity.