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In modern nuclear physics, a special group of nuclei located close to the drip line named halo nuclei has received tremendous attention due to their unique cluster structure. These nuclei exhibit large matter radii and are qualitatively described as a compact core surrounded by a diffuse halo which is formed by the loosely-bound valence nucleon(s). Their existence breaks down the consistent predictions by the classical shell model and challenges nuclear-structure calculations. To understand this exotic feature from first principles, lots of efforts have been undertaken by nuclear physicists during the past decades. One of the most successful probes to look into these questions is the (d,p) transfer which has been proved to be a very powerful tool to extract single-particle properties of nuclei and hence is ideal to study one-neutron halo nuclei.The main topic of this work is to improve the reliability of the nuclear-structure observables extracted from transfer reactions. In one of our works [Phys. Rev. C 98, 054602 (2018)], the experiment done by Schmitt et al. on the $^{10}$Be(d,p)$^{11}$Be transfer reaction at four beam energies [Phys. Rev. Lett. 108, 192701 (2012)] is reanalyzed. In order to probe only the halo of the nucleus which is represented by the asymptotic normalization coefficient (ANC), the beam energy and angular ranges at which such reaction is strictly peripheral have to be determined. These peripheral conditions are systematically identified by coupling a Halo effective field theory (EFT) description of the $^{11}$Be nucleus at leading order (LO) with the adiabatic distorted wave approximation (ADWA) to model the transfer. The results suggest that focussing on the transfer data collected with low beam energies and at forward scattering angles ensures the peripherality of the reaction and hence is the best way to reliably extract the ANC. The resulting values of ANC are (0.785 ± 0.030) fm$^{-1/2}$ for the ground state and (0.135 ± 0.005) fm$^{-1/2}$ for the first excited state. These values are in excellent agreement with the values predicted by ab initio calculations (0.786 fm$^{-1/2}$ for the ground state and 0.129 fm$^{-1/2}$ for the excited state) [Phys. Rev. Lett. 117, 242501 (2016)]. An alternative way to explore the sensitivity of transfer calculations to the short-range physics of the $^{10}$Be-n wave function using Halo EFT is offered by the supersymmetry (SuSy) method. With this method, the SuSy partner of the original wave function can be generated which shares the same asymptotic behavior but exhibits a very different internal part. Feeding those wave functions into the transfer calculations, the results confirm the above findings with respect to the peripherality of the $^{10}$Be(d,p) transfer.This method has then been extended to study another one-neutron halo nucleus: $^{15}$C which is important in nuclear astrophysics. Its ANC is extracted from the cross sections of the $^{14}$C(d,p) transfer measured by Mukhamedzhanov et al. [Phys. Rev. C, 84, 024616 (2011)]. The values obtained are (1.26 ± 0.02) fm$^{-1/2}$ and (0.056 ± 0.001) fm$^{-1/2}$ for the ground state and first excited state of $^{15}$C, respectively. Especially for the ground state case, again, a perfect agreement is reached between our result and the one predicted by Navrátil et al. (C$_{1/2+}$ = 1.282 fm$^{-1/2}$) in an ab initio calculation. Relying on the inferred ANC value, it enables us to fit an effective $^{14}$C-n interaction at NLO in Halo EFT, which has been used later in other reaction calculations, such as Coulomb breakup and radiative capture [Phys. Rev. C 100, 044615 (2019)].We have also looked at the extension of this idea to resonant states. After an analogous analysis using a bin description, it is figured out that the resonant width plays a key role in determining the magnitude of the cross sections for such transfers. Its effect on resonance can be comparable to that of the ANC on bound states. But the associated uncertainty is larger than that in the case of bound state.In collaboration with Prof. Obertelli, we have studied the potential use of sub-Coulomb (d,p) transfer to investigate the possible presence of a halo structure in the excitation spectrum of medium to heavy nuclei. Based on the hypothetical case of $^{95}$Sr, the dependencies of the transfer calculation on several crucial parameters including Q-value, nuclear spin and beam energy have been tested to understand better how the halo feature could be revealed by measuring transfer cross sections. The feasibility of this idea requires an accurate theoretical prediction and sensitive detection systems.On the experimental side, efforts have been made to progress in the data analysis of the IS561A experiment on $^{9}$Li(d,p) transfer performed at HIE-ISOLDE, CERN. Thanks to the preprocessing of the acquired data done by Jesper Halkjær Jensen (Aarhus), the necessary information on the elastic scattering channel ($^{9}$Li + d) has been successfully collected and matches well with our theoretical calculation. Due to some practical problems happening during the measurement which would propagate to the analysis and result in a low statistics, the extraction of the (d,p) channel will require further detailed analyses. To make up for this, the available data measured by Jeppesen et al. [Phys. Lett. B, 642(5): 449 - 454, 2006] and Cavallaro et al. [Phys. Rev. Lett. 118, 012701 (2017)] are taken into account to check in those cases the validity of the chosen model which has already been used to study the resonance of $^{11}$Be. The outcome suggests that the method we use is a fast and efficient option to simulate the resonance during the transfer. For the non-resonant part, choosing the prior form of the transition matrix instead of the post one is better suited.