Bars are common in disc galaxies along with many associated structures such as disc-like bulges, boxy/peanut bulges, rings, etc. They are a sign of maturity of disc galaxies and can play an important role in their evolution. In this thesis, I investigate the specific role bars play in quenching the star formation in, and shaping of their host galaxies. In order to test how bars affect their host galaxies, I study the discs, bars and bulges of what is currently the largest sample of barred galaxies (~3,500), selected with visual morphologies from the Galaxy Zoo project. I perform multi-wavelength and multi-component photometric decomposition, with the novel GALFITM software. With the detailed structural analysis I obtain physical quantities such as the bar- and bulge-to-total luminosity ratios, effective radii, Sérsic indices and colours of the individual components. I find a clear difference in the colours of the components, the discs being bluer than the bars and bulges. An overwhelming fraction of bulge components have Sérsic indices consistent with being disc-like bulges. I compare the barred galaxies with a mass- and environment-matched volume-limited sample of unbarred galaxies, finding that the discs of unbarred galaxies are bluer compared to the discs of barred galaxies, while there is only a small difference in the colours of the bulges. I suggest that this is evidence for secular evolution via bars that leads to the build-up of disc-like bulges and to the quenching of star formation in the galaxy discs. I identify a subsample of unbarred galaxies that are better fitted with an additional component, identified as an inner lens/oval. I find that their structural properties are similar to barred galaxies, and speculate that lenses might be former bars. Using the decompositions, I identify a sample of 271 late-type galaxies with curious bars that are off-centre from the disc. I measure offsets up to 2.5 kpc between the photometric centres of the stellar disc and stellar bar, which are in good agreement with predictions from simulations of dwarf-dwarf tidal interactions. The median mass of these galaxies is 109.6 M⊙, and they are similar to the Large Magellanic Cloud, which also has an offset bar. Very few high mass galaxies with significant bulges show offsets, thus I suggest that the self-gravity of a significant bulge prevents the disc and bar from getting displaced with respect to each other. I conduct a search for companions to test the hypothesis of tidal interactions, but find that a similar fraction of galaxies with offset bars have companions within 100 kpc as galaxies with centred bars. Since many of these galaxies appear isolated, interactions might not be the only way to produce an offset bar. One suggested alternative is that the dark matter haloes surrounding the galaxies are lopsided, which distorts the potential, and imprints the lopsidedness and offsets onto the galaxy discs. I investigate the asymmetries in the kinematics of a subsample of such galaxies using data from the MaNGA survey, and find that the perturbations in the haloes are ~ 6% for both galaxies with off-centre and centred bars. I also measure the amplitude of non-circular motions in the outer discs due to an oval potential and find only minor departures from circularity, suggesting that the dark matter haloes are consistent with being spherical (axis ratio q ≳ 0.96). Therefore, the lopsidedness of the dark matter haloes cannot be the origin of the offsets. Either small companions are missed due to the incompleteness of the Sloan Digital Sky Survey spectroscopic survey, or interactions with dark matter satellites might explain the offsets. Modeling the kinematics of these galaxies, I find that the Hα gas rotation is centred closer to the centre of the bar than the centre of stellar rotation, suggesting that, in general, the bars are located closer to the dynamical centres of these galaxies than the discs. This implies that the discs are offset in these galaxies, not the bars. If offsets are characteristic of low mass galaxies only, high mass galaxies show vertically extended bars, known as boxy/peanut bulges. I investigate, for the first time, the formation and evolution of these structures associated to bars, from z≈0 to z=1. I compare two samples of moderately inclined galaxies with masses M* > 1010 M⊙, imaged by the Sloan Digital Sky Survey and the Hubble Space Telescope. Using a novel technique to classify bar isophotes, and based on the visual inspection of three expert astronomers, I find an evolving fraction of galaxies having boxy/peanut bulges from 30% at z≈0 to ~ 0% at z=1, and a strong correlation with stellar mass. I find 26 galaxies (15 at higher redshifts) in the phase of bar buckling, the mechanism proposed to form boxy/peanut bulges. The peak redshift of buckling is z≈0.75, where the bar buckling fraction is 4 times higher than in the local Universe. My observations suggest that many, if not all, of the boxy/peanut bulges are formed via buckling, ~ 2 Gyr after bar formation, with the buckling phase lasting for approximately 0.8 Gyr. I discuss my findings in the context of the evolution of barred galaxies and propose ideas for future work - applying similar decomposition techniques to higher redshift, and better resolution datasets, using integral field spectroscopic data to study the stellar populations of barred galaxies in greater detail, as well as a novel project to identify large nuclear discs in galaxies.