The study of magnetic fields in molecular clouds formed in various environments have enormous potential towards understanding the underlying physics behind the role played by the magnetic fields in the formation of molecular clouds and the subsequent star formation. The closer and isolated molecular clouds provide the fascinating laboratories where the importance of magnetic fields can be explored towards ongoing activities like evolution of the cloud and star formation. This needs a extensive study of magnetic fields on the large scales of these regions. Therefore, in general, the focus of this thesis is to explore the magnetic fields morphology and strength in various environments of molecular clouds to understand the open issue of the role played by magnetic fields in interstellar medium (ISM). The regions where we have mapped the magnetic fields are broadly classified into the categories viz. triggered star forming and spontaneous star forming sites. In triggered star forming regions, we have chosen the multiple bright-rimmed clouds (BRCs) and cometary globules (CGs) associated to some HII regions surrounded by a high mass star in the center. When a massive star forms, it photoionizes the surroundings, forming an HII region which display highly irregular structures such as BRCs. The radiation driven implosion process explains the photoionization induced collapse of a dense, isolated cloud that is illuminated from one side by a source of ionizing radiation. In the presence of magnetic fields, the dynamical evolution of the globule and ionized gas streaming out of the globule surface get modified significantly depending on the strength and the orientation (w.r.t the direction of incoming ionizing radiation) of the magnetic field. These HII regions are selected because of their structural simplicity and proximity to the sun. The advantage of studying multiple BRCs associated with the same HII region is that one can perform a comparative study of the magnetic field morphology at various locations of the HII region w.r.t. the direction of the ionizing radiation from the central source. Magnetic fields in a significant number of BRCs and CGs located in northern hemisphere have not been explored comprehensively. In order to examine the role played by the magnetic fields in the formation and further evolution of structures like BRCs and CGs on the periphery of HII regions, an attempt of mapping the large scale magnetic fields has been made using optical, near-IR (NIR) and submillimeter (submm) polarisation techniques. The observed polarisation is caused by the selective extinction of the light as it passes through the elongated dust grains that are aligned with their minor axis parallel to the local magnetic fields of the cloud. Moreover, our investigations reveal the effects of ionising radiation on the inherent magnetic field structures in these regions. In one part of the thesis, the plane of the sky magnetic fields morphologies in BRCs and CGs associated to HII regions Sh 2-185, Sh 131, Sh 236, Sh 126, Orion and Ophiuchus molecular clouds, are studied. Various orientations of fields lines w.r.t. the incoming high energy radiation from the nearby ionising source have been found. Based on these orientation, the evolution of BRCs and CGs are attempted to be understood by comparing the observational results with the prevailed magnetohydrodynamics (MHD) simulations. Firstly, we categorized the results of observations of the magnetic fields direction in BRCs and CGs as parallel, perpendicular and inclined w.r.t. the incoming ionising radiation. Using these observations and comparison with simulations, the radiation driven implosion (RDI) process has been attempted to be understood in this work. Along with the evolution of globules in context of the magnetic fields, we have also mapped the ionized gas using radio continuum observations towards a open cluster NGC 1893 containing a number of O type stars. The magnetic field structure have been found responsible for the morphology of these clouds. The fields lines are found to be following the ionised gas mapped using the radio observations. It has been widely accepted that the magnetic fields play an important role in the spontaneous star formation process. The influence of magnetic fields in all stages of cloud and star formation is still unclear. In a magnetic field dominated scenario for isolated low-mass star formation, the cores are envisaged to gradually condense out of a magnetically subcritical background cloud, through ambipolar diffusion. To under- stand the evolution of magnetic fields in the cores of different ages (ages determined based onto the chemical evolution), we have studied the magnetic fields in a number of prestellar cores. Magnetic fields morphology in some of the cores harboring very low luminosity objects (VeLLOs) have also been made in this thesis. These studies will help in understanding the standard models of low mass star formation and key role played by the magnetic fields in these processes. In order to understand the disk formation in the low mass stars, we have studied the magnetic field structure and following alignment/misalignment between the mean magnetic field direction and the rotation axis (the outflow axis is presumed to be the rotation axis of the core) in a core with a proto-brown dwarf candidate as a central object. Magnetic field strength have been estimated using the modified Chandrasekhar-Fermi (CF) relation. The magnetic fields direction in general is found to be parallel to the minor axes and aligned with the outflow direction from the central object. These result support the standard models of low mass star formation. This thesis also contains a small catalog containing fainter polarized standard stars available in the fields of already found brighter polarized standard stars described in the literature. These brighter standard stars, when observed with big aperture telescope, get saturated. Hence the fainter standard stars listed in this thesis will solve the issue of the saturation of the stars.