This thesis presents experimental and related theoretical studies of pyrochlore titanate oxides, boron nitride nanotubes, and multiferroic bismuth ferrite. We have investigated these systems at high pressures and at low temperatures using Raman spectroscopy. Below, we furnish a synoptic presentation of our work on these three systems. In Chapter 1, we introduce the systems studied in this thesis, viz. pyrochlores, boron nitride nanotubes, and multiferroic BiFeO3, with a review of the literature pertaining to their structural, electronic, vibrational, and mechanical properties. We also bring out our interests in these systems. Chapter 2 includes a brief description of the theory of Raman scattering and infrared absorption. This is followed by a short account of the experimental setups used for Raman and infrared measurements. We also present the technical details of high pressure technique including the alignment of diamond anvil cells, gasket preparation, calibration of the pressure, etc. Chapter 3 furnishes the results of our pressure-and temperature-dependent studies of pyrochlore oxides which has been divided into eight different parts. In recent years, magnetic and thermodynamic properties of pyrochlores have received a lot of attention. However, not much work has been reported to address the quasiparticle excitations, e.g., phonons and crystal-field excitations in these materials. A material that shows exotic magnetic behavior and high degree of degenerate ground states can be expected to have low-lying excitations with possible couplings with phonons, thereby, finger-printing various novel properties of the system. Raman and infrared absorption spectroscopies can, therefore, be used to comprehend the novel role of phonons and their role in various phenomena of frustrated magnetic pyrochlores. Recently, there have been reports on various novel properties of these systems; for example, Raman and absorption studies [Phys. Rev. B 77, 214310 (2008)] have revealed a loss of inversion symmetry in Tb2Ti2O7 at low temperatures which has been suggested as the key reason for this frustrated magnet to remain in spin-liquid state down to 70 mK. Powder neutron-diffraction experiments [Nature 420, 54 (2002)] have shown that an application of isostatic pressure of about 8.6 GPa in spin-liquid Tb2Ti2O7 induces a long-range magnetic order of the Tb3+ spins coexisting with the spin-liquid phase ascribing this transition to the breakdown of the delicate balance among the various fundamental interactions. Moreover, Raman and x-ray studies have shown that Tb2Ti2O7,Sm2Ti2O7,and Gd2Ti2O7 undergo a structural transition followed by an irreversible amorphization at very high pressures (~ 40 GPa or above) [Appl. Phys. Lett. 88, 031903 (2006)]. In this chapter, therefore, we present our temperature-and pressure-dependent Raman studies of A2Ti2O7 pyrochlores, where ‘A’ is a trivalent rare-earth element (A = Sm, Gd,Tb, Dy,Ho, Er,Yb, and Lu; and also Y). Since all the group theoretically predicted Raman modes of this cubic lattice are due to oxygen vibrations only, in Part (A), we revisit the phonon assignments of pyrochlore titanates by performing Raman measurements on the O16 /O18 − isotope based Dy2Ti2O7 and Lu2Ti2O7 and find that the vibrations with frequencies below 250 cm−1 do not involve oxygen atoms. Our results lead to a reassignment of the pyrochlore Raman phonons thus proposing that the mode with frequency ~ 200 cm−1, which has earlier been known as an F2g phonon due to oxygen vibration, is a vibration of Ti4+ ions. Moreover, we have performed lattice dynamical calculations using Shell model that help us to assign the Raman phonons. In Part (B), we have explored the temperature dependence of the Raman phonons of spin-ice Dy2Ti2O7 and compared with the results of two non-magnetic pyrochlores, Lu2Ti2O7 and Y2Ti2O7. Our results reveal anomalous red-shift of some of the phonons in both magnetic and non-magnetic pyrochlores as the temperature is lowered. The phonon anomalies can not be understood in terms of spin-phonon and crystal field transition-phonon couplings, thus attributing them to phonon-phonon anharmonic interactions. We also find that the anomaly of the disorder activated Ti4+ Raman vibration (~ 200 cm−1) is unusually high compared to other phonons due to the large vibrational amplitudes of Ti4+-ions rendered by the vacant Wyckoff sites in their neighborhood. Later, we have quantified the anharmonicity in Dy2Ti2O7. We have extended our studies on spin-ice compound Dy2Ti2O7 by performing simultaneous pressure-and temperature-dependent Raman measurements, presented in Part (C). We show that a new Raman mode appears at low temperatures below TC ~ 110 K, suggesting a structural transition, also supported by our x-ray measurements. There are reports [Phys. Rev. B 77, 214310 (2008), Phys.Rev.B 79, 214437 (2009)] in the literature where the new mode in Dy2Ti2O7 at low temperatures has been assigned to a crystal field transition. Here, we put forward evidences that suggest that the “new” mode is a phonon and not a crystal field transition. Moreover, the TC is found to depend on pressure with a positive coefficient. In Part (D), we have presented our results of temperature-and pressure-dependent Raman and x-ray measurements of spin-frustrated pyrochlores Gd2Ti2O7, Tb2Ti2O7,and Yb2Ti2O7. Here, we have estimated the quasiharmonic and anharmonic contributions to the anomalous change in phonon frequencies with temperature. Moreover, we find that Gd2Ti2O7 and Tb2Ti2O7 undergo a subtle structural transition at a pressure of ~ 9 GPa which is absent in Yb2Ti2O7. The implication of this structural transition in the context of a long-range magnetically ordered state coexisting with the spin-liquid phase in Tb2Ti2O7 at high pressure (8.6 GPa) and low temperature (1.5 K), observed by Mirebeau et al. [Nature 420, 54 (2002)], has been discussed. As we have established in the previous parts that the anomalous behavior of pyrochlore phonons is due to phonon-phonon anharmonic interactions, we have tuned the anharmonicity in the first pyrochlore of the A2Ti2O7 series, i.e., Sm2Ti2O7,by replacing Ti4+-ions with bigger Zr4+-ions, presented in Part (E). Our results suggest that the phonon anomalies have a very strong dependence on the ionic size and mass of the transition element (i.e., the B4+-ion in A2B2O7 pyrochlores). We have also observed signatures of coupling between a phonon and crystal-field transitions in Sm2Ti2O7. In Part (F), we have studied spin-ice compound Ho2Ti2O7 and compared the phonon anomalies with the stuffed spin-ice compounds, Ho2+xTi2−xO7−x/2 by stuffing Ho3+ ions into the sites of Ti4+ with appropriate oxygen stoichiometry. We find that as more and more Ho3+-ions are stuffed, there is an increase in the structural disorder of the pyrochlore lattice and the phonon anomalies gradually disappear with increasing Ho3+-ions. Moreover, a coupling between phonon and crystal field transition has also been observed. In Part (G), we have examined the temperature dependence of phonons of “dynamical spin-ice” compound Pr2Sn2O7 and compared with its non-pyrochlore (monoclinic) counterpart Pr2Ti2O7. Our results conclude that the anomalous behavior of phonons is an intrinsic property of pyrochlore structure having inherent vacant sites. We also find a coupling between phonon and crystal-field transitions in Pr2Sn2O7. In the last part of this chapter, Part (H), we present our Raman studies of Er2Ti2O7. Here, we show that in addition to the anomalous phonons, there are modes that originate from photoluminescence transitions and some of these luminescence lines show anomalous temperature dependence which have been understood using the theory of optical dephasing in crystals, developed by Hsu and Skinner [J. Chem. Phys. 81, 1604 (1984)]. Temperature dependence of a few Raman modes and photoluminescence bands suggest a phase transition at 130 K. In Chapter 4, we furnish our pressure-dependent Raman studies of boron nitride multi-walled nanotubes (BNNT) and hexagonal boron nitride (h-BN) and compare the results with those of their carbon counterparts. Using Raman spectroscopy, we show that BNNT undergo an irreversible transition at ~ 12 GPa while the carbon counterpart, multi-walled carbon nanotubes, show a similar transition at a much higher pressure of ~ 51 GPa. In sharp contrast, the layered form of both the systems (i.e. h-BN and graphite) undergo a hexagonal to wurtzite phase at nearly similar pressure (~ 13 GPa of h-BN and ~ 15 GPa for graphite). A molecular dynamical simulation on boron nitride single-walled nanotubes has also been undertaken that suggests that the polar nature of the B−N bonds may be responsible for the irreversibility of the pressure-induced transformations. It is interesting to see that in hexagonal phase both the systems have almost similar mechanical property, but once they are rolled up to make nanotubes, the property becomes quite different. Chapter 5 presents the temperature dependence of the Raman modes of multiferroic thin films of BiFeO3 and Bi0.7Tb0.2La0.1O3. Though there have been several Raman investigations of BiFeO3 in literature, here we emphasize the observation of unusually intense second order Raman phonons. Our results have motivated Waghmare et al. to suggest a theoretical model to explain the anomalously large second order Raman tensor of BiFeO3 in terms of an incipient metal-insulator transition. In Chapter 6, we summarize our findings on the three different systems, namely, pyrochlores, boron nitride nanotubes, and BiFeO3 and highlight a few possible experiments that may be undertaken in future to have a better understanding of these systems.