This thesis explores low-frequency radio behaviour of supernovae and supernova remnants. Supernovae are the explosive end stages of stellar evolution. The interaction of the supernova ejecta with its surrounding circumstellar material results in synchrotron emission which can be studied using radio observations. The past decade has seen a greater exploration of the low frequency radio sky. At low radio frequencies, the ionosphere causes major problems. Specialised calibration and imaging techniques, along with new technologies for data handling have paved the way for science at low frequencies. The LOw Frequency ARray (LOFAR) is based in the Netherlands and is the focus of this thesis. In operation for over a decade now, LOFAR explores frequencies between 10 and 240 MHz. The LOFAR Two-metre Sky Survey (LoTSS) has already mapped the northern sky with 4.5 million radio sources in its latest data release covering 27% of the northern sky. In addition, LOFAR has stations across Europe forming the International LOFAR Telescope (ILT). Processing data with the ILT using standardised pipelines is a major recent development in doing Very Long Baseline Interferometry (VLBI) with LOFAR, resulting in the highest resolution possible at these frequencies. This is true even when the Square Kilometre Array (SKA) comes online. The upcoming SKA will be the world's largest radio telescope and has been a major driver of low frequency radio sky exploration.

For explosive transients like supernovae, low radio frequencies remain unexplored and present exciting possibilities on understanding absorption mechanisms at play using the low-frequency radio turnover. In Paper I, we present the first subarcsecond resolution image of the nearby galaxy M51 with the ILT. We especially focus on three known supernovae in M51 making it the first detailed study of supernovae with LOFAR. One key finding is that the LoTSS flux density for SN 2011dh is about five times higher than the flux density with the ILT image, which would affect the absorption scenario, and in turn derivation of mass-loss parameters for the supernova. This is partially explained by the fact that the ILT filters out diffuse emission, and that the beam fit to the source in LoTSS is bigger than the image beam size. In Paper II, we present the first LOFAR image of the centre of M31. We report upper-limits on the historical SN 1885A which has never been detected in the radio. Using VLA data we are also able to characterise three other remnants in the field and report spectral indices, ages, shock velocities and morphology. A key takeaway from this work is that, from estimations of the flux density and radius of the forward shock of SN 1885A, we believe the remnant is likely at the limit of detection with the ILT, given the instrument's improved noise and resolution. In Paper III, we focus on three supernovae SN 2006X and SN 1979C in the nearby galaxy M100 and SN 1986J in NGC 891. Using LoTSS data of M100 that is not yet publicly available, we report upper limits for the Type Ia SN 2006X. A key finding for SN 1979C is a marked steepening of the radio spectra at late times in our data from 2019-2020. This contradicts previous findings that reported a spectral flattening which is expected in case of a central compact object. 

Such studies help us bridge the gap between our current understanding of various objects in the radio sky and what instruments such as the SKA will bring with it in the future.