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Millisecond pulsars - highly magnetised neutron stars rotating with millisecond periods - are usually observed in binary systems as they are 'spun up' to such fast periods by the accretion of matter from their companion. The 'spider' class of binary contains a millisecond pulsar and a low mass, degenerate companion in a tight orbit which is irradiated by the pulsar wind, resulting in distinct observable properties across the whole electromagnetic spectrum. The first part of this research presents new optical photometry of two systems, PSR J1023+0038 and PSR J1227-4853, which display transitions between the aforementioned accretion phase and the spider phase. We find that through modelling these data we gain insights into the nature of this transition. The second concerns the search for new spider systems with the creation of a classification pipeline for the new Gravitational-wave Optical Transient Observatory telescope project, employing periodicity search and machine learning classification techniques. We discuss the application of this pipeline to commissioning data from this fledgling project, and how the shortfalls we encountered can be overcome.

Pulsars are named for the periodic pulse of electromagnetic energy we detect from point sources in the sky and are considered exceptionally good, but not perfect, cosmic clocks. We use sensitive radio telescopes to measure pulse time-of-arrivals (ToAs) and construct pulsar timing models containing rotational, astrometric and stellar binary system parameters. Pulsar timing compares measured ToAs with the predictions from the model and analysing the differences can provide insights into a wide range of astrophysical phenomena. The key instrument in pulsar observations is the Pulsar Timing System (PTS) and in this thesis we describe our development of two new pulsar timing systems. The first is a robust, low cost, next generation system using consumer grade GPUs as the compute engine and we have instruments installed in Ghana and at Jodrell Bank Observatory in the UK. We consider the apparent relationship between pulsar characteristic age and spectral index and we seek to make pulsar flux density measurements at 5GHz and 6.7GHz (in C-band) using the AVN radio telescope at Kuntunse in Ghana to explore this relationship further. We also consider searching for pulsars in the Galactic centre region where the potential benefits of using pulsars to probe the region and SgrA* would be very significant. Our second pulsar timing system combines the observations from the six medium sized, geographically dispersed, e-MERLIN telescopes into a single incoherent beam providing increased sensitivity to pulsar signals. We are making pulsar timing observations of eight pulsars that exhibit transient behaviour in the form of glitches (a sudden increase in the rate of rotation) or mode-switching (changes to the pulse profile). The e-MERLIN facility now offers a 'Pulsar LOFT-e Mode' as an option for external researchers based on our work on this PTS.

The radio sky is not static. Time-variable radio emission is induced in the Earth's atmosphere, and is emitted by other bodies in our Solar System, the Milky Way, and in galaxies beyond our own. It may vary on timescales which span a range from years to nanoseconds. Technological advances are increasingly allowing radio astronomers to study the radio transient events which occur on the shortest of these timescales. Of particular interest are the emission from pulsars, and an extragalactic population of fast radio bursts (FRBs), which was discovered just over a decade ago. The signals measured from both on Earth are affected by matter they traverse en-route to us. Through their dispersion measures (DMs), pulsars have enabled radio astronomers to model the Milky Way's electron distribution. Likewise, extragalactic FRBs may potentially probe matter which lies between galaxies, and that of their own hosts. To maximise the use of such distant events, the expansion of the Universe must be accounted for. The recession of other galaxies and the phenomenon of cosmological time dilation both measurably impact observed signatures of FRBs. Both effects may be accounted for by accurate deduction of FRB source's redshifts. This is driving radio astronomers to develop radio facilities with the high sensitivities and large fields of view necessary for detection of FRBs in greater numbers, and with precise enough angular resolutions to associate them with host galaxies and thus obtain their redshifts. So far only one FRB, by virtue of its observed repeating behaviour, has been localised. The e-MERLIN interferometer is a six-dish array of radio telescopes in the United Kingdom. Its long baselines between dishes provide it with the means to localise to sub-arcsecond accuracy any FRBs it may detect. This thesis details the Localisation of Fast Transients with e-MERLIN (LOFT-e) upgrade to e-MERLIN, developed by the author to enable high time-resolution studies with the instrument. The first successful observations of pulsars and single pulses from Rotating RAdio Transients (RRATs) are presented, techniques developed to increase its sensitivity via incoherent beamforming are detailed and the instrument's RFI environment is discussed. Finally, a framework to allow DM-redshift analysis of FRBs which may never be localised is introduced.

In this thesis we present a detailed study into the poorly understood eclipse phenomena of Galactic field eclipsing pulsar binaries; known as the black widows and redbacks. The work is primarily based on a large set of radio-frequency observations, made up of both dedicated campaigns and archival data from a number of telescope facilities, in order to markedly increase the quality and volume of evidence to constrain future theoretical models, and as such, further our understanding. Here, we present the work in four interlinked parts: Firstly, we observed and investigated the eclipses of PSR J1810+1744, a near-unexplored black widow, at low-radio-frequencies. In this frequency domain the pulsar is bright, and the propagation effects that are vital to understanding the eclipse medium become more pronounced. Using these observations we constrain the mechanisms responsible for the eclipse and the mass loss rate from the companion star. Secondly, we performed an analysis of a well studied black widow, PSR J2051-0827, collating a large volume of data on its eclipses covering over a decade in time and frequencies from 100 MHz to 4 GHz. This time and frequency coverage is the most extensive used in a single dedicated eclipse study of a pulsar, and reveals variability in the eclipse phenomena on a range of timescales. Using observations sensitive to the polarisation of the pulsar radiation, we constrain the magnetic field strengths in the eclipse region. Stemming from our work on PSR J1810+1744, we conducted a dedicated low-frequency study of two more pulsars: redback PSR J1816+4510 and black widow PSR B1957+20. These two systems have similar orbital properties, however their companion stars differ in mass by nearly an order of magnitude. We compare the eclipse phenomena in both, finding remarkable similarities, seemingly independent of the companion masses. Finally, bringing together the four pulsars studied throughout this thesis, and adding a further redback - PSR J2215+5135 - we perform an analysis of the eclipse durations as a function of the pulsar radiation frequency. The results show that for all of the pulsars the eclipse widths scale inversely with frequency, however the rate at which they do so varies between systems. We discuss further complexities such as temporal variability of the eclipses and differing relationships acting at low- and high-frequencies.