Pulsars are renowned for exceptional rotational stability. Due to their strong magnetic fields, pulsars lose rotational energy over time and, in general, their slow-down is smooth and continuous. Not all pulsars however, show such long-term stability. Two types of timing irregularity are common - timing noise, thought to be related to transitions in the spin-down rate, and glitches. In this thesis we describe simulations undertaken to understand the spin-down transitioning scenarios we are able to resolve with current pulsar timing programmes. We inject spin-down transitions into simulated pulse times-of-arrival and then attempt to recover the transitions using standard pulsar timing techniques. We find that we are potentially insensitive to a large diversity of transitioning phenomena and show that using mode-switching as a marker of spin-down transitions can, in some cases, enhance the probability of resolving transitions. We have also expanded on previous work which revealed spin-down variations in 17 pulsars that show timing noise. By using a Gaussian processes (GP) method to model timing residuals and profile variations, we have confirmed the transitions already observed and revealed new variations in 8 years of further monitoring. We confirm that 7 of these sources exhibit correlated spin-down and profile changes and describe a new example of such variability in a further source. Finally, we describe our detection and measurement of the largest glitch observed in the Crab pulsar. On 2017-11-07, the Crab pulsar's spin-frequency increased by 1.530e-05 Hz, part of which was resolved in time. We discuss the possible prevalence of partially resolved spin-ups across the pulsar population and find a possible correlation between the glitch size and waiting time. We discuss this glitch in the context of other Crab pulsar glitches and compare the Crab's glitch activity with that of other well-studied glitching pulsars such as the Vela pulsar. Comparable observations of many more pulsars with new generations of telescopes are encouraged as they will dramatically improve our understanding of glitch parameter space and provide new insights into the nature of the neutron star interior.