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The detection of Mpc scale diffuse radio emission in galaxy clusters provides evidence that cosmic ray electrons, as well as cluster scale magnetic fields are present in clusters. As such, radio observations of clusters provide a unique opportunity to study the non-thermal populations of the intra-cluster medium. Observations of Faraday rotation in sources embedded in cluster and group environments offers an additional method for probing the cluster/group magnetic field. In this thesis I present low frequency radio observations of multiple galaxy clusters in order to investigate the nature of diffuse radio emission present in many clusters. I also present observations of the giant radio galaxy NGC 6251 and discuss both the source properties as well as the host group environment. In Chapter 1 of this thesis I review the current understanding of galaxy clusters, groups and radio galaxies. I also describe some of the astrophysical processes important to this thesis. In Chapter 2 I discuss the interferometry and the process of calibrating interferometric data. I also describe some of the techniques used later in the thesis such as QUfitting and RM synthesis. In Chapter 3 I present my observations of the massive merging galaxy cluster MACSJ2243.3-0935. I report the discovery of a radio halo in MACSJ2243.3-0935, as well as a new radio relic candidate, using the Giant Meterwave Radio Telescope and the KAT-7 telescope. The radio halo is coincident with the cluster X-ray emission and has a largest linear scale of approximately 0.9 Mpc. I measure a flux density of $10.0\pm 2.0\, \rm mJy$ at 610 MHz for the radio halo. I discuss equipartition estimates of the cluster magnetic field and constrain the value to be of the order of $1\, \rm \mu G$. The relic candidate is detected at the cluster virial radius where a filament meets the cluster. The relic candidate has a flux density of $5.2\pm 0.8\, \rm mJy$ at 610 MHz. I discuss possible origins of the relic candidate emission and conclude that the candidate is consistent with an infall relic. In Chapter 4 I present my GMRT observations at 610 MHz of 3 disturbed galaxy clusters, A07, A1235 and A2055. No diffuse emision was observed any of the three clusters. In order to place upper limits on the radio halo power in these clusters I have injected simulated halos at difffent radio powers into the uvdata. A07 has a radio halo upper limit of $P_{\rm 610MHz}=1.5\times10^{24}$ W Hz$^{-1}$. A2055 has a radio halo upper limit of $P_{\rm 610MHz}=1.8\times10^{24}$ W Hz$^{-1}$. A1235 has a radio halo upper limit of $P_{\rm 610MHz}=5.8\times10^{23}$ W Hz$^{-1}$. These limits are below the $P_{610}-L_{\rm X}$ relation and rule out bright radio halo in these clusters. I have identified these clusters as potential hosts for Ultra Steep Spectrum Radio Halo (USSRH). Observations with LOFAR should be capable of confirming whether or not these clusters host USSRH. In Chapter 5 I present observations of the giant radio galaxy NGC 6251 with LOFAR HBA. NGC 6251 is a giant radio galaxy with a borderline FRI/FRII morphology located in a poor group. The images presented in this chapter are the highest sensitivity and resolution images of NGC 6251 at these frequencies to date. Analysis of the low frequencies spectral index did not reveal any change in the low frequency spectra when compared with the higher frequency spectral index. NGC 6251 is found to be either at equilibrium or slightly electron dominated, similar to FRII sources. I calculated the ages of the low surface brightness extension of the northern lobe and the backflow of the southern lobe, which are only clearly visible at these low frequencies, to be 205 Myr$.