∼$6\%$ of all known pulsars have been observed to exhibit sudden spin-up events, known as glitches. For more than fifty years, these phenomena have played an important role in helping to understand pulsar (astro)physics. Based on the review of pulsar glitches search method, the progress made in observations in recent years is summarized, including the achievements obtained by Chinese telescopes. Glitching pulsars demonstrate great diversity of behaviours, which can be broadly classified into four categories: normal glitches, slow glitches, glitches with delayed spin-ups, and anti-glitches. The main models of glitches that have been proposed are reviewed and their implications for neutron star structure are critically examined regarding our current understanding. Furthermore, the correlations between glitches and emission changes, which suggest that magnetospheric state-change is linked to the pulsar-intrinsic processes, are also described and discussed in some detail.

Treatment of the vortex motion in the superfluids of the inner crust and the outer core of neutron stars is a key ingredient in modelling a number of pulsar phenomena, including glitches and magnetic field evolution. After recalculating the microscopic vortex velocity in the inner crust, we evaluate the velocity for the vortices in the outer core for the first time. The vortex motion between pinning sites is found to be substantially faster in the inner crust than in the outer core, $$v_0^{\rm crust} \sim 10^{7}{{\rm \,cm\,s}^{-1}} \gg v_0^{\rm core} \sim 1{{\rm \,cm\,s}^{-1}}$$. One immediate result is that vortex creep is always in the nonlinear regime in the outer core in contrast to the inner crust, where both nonlinear and linear regimes of vortex creep are possible. Other implications for pulsar glitches and magnetic field evolution are also presented.

Timing observations of rapidly rotating neutron stars revealed a great number of glitches, observed both from canonical radio pulsars and magnetars. Among them, 76 glitches have shown exponential relaxation(s) with characteristic decay times ranging from several days to a few months, followed by a more gradual recovery. Glitches displaying exponential relaxation with single or multiple decay time constants are analysed in terms of a model based on the interaction of the vortex lines with the toroidal arrangement of flux tubes in the outer core of the neutron star. Model results agree with the observed timescales in general. Thus, the glitch phenomenon can be used to deduce valuable information about neutron star structure, in particular on the interior magnetic field configuration which is unaccessible from surface observations. One immediate conclusion is that the magnetar glitch data are best explained with a much cooler core and therefore require that direct Urca type fast cooling mechanisms should be effective for magnetars.

We present timing solutions from the Fermi-LAT observations of gamma-ray pulsars PSR J0835 − 4510 (Vela), PSR J1023−5746, PSR J2111+4606, and PSR J2229+6114. Data ranges for each pulsar extend over a decade. From data analysis, we have identified a total of 20 glitches, 11 of which are new discoveries. Among them, 15 glitches are large ones with Δν/ν ≳ 10⁻⁶. PSR J1023−5746 is the most active pulsar with glitch activity parameter being A_g = 14.5 × 10⁻⁷ yr⁻¹ in the considered data span and should be a target for frequently glitching Vela-like pulsars in future observations. We have done fits within the framework of the vortex creep model for 16 glitches with Δν/ν ≳ 10⁻⁷. By theoretical analysis of these glitches, we are able to obtain important information on the structure of neutron star, including moments of inertia of the superfluid regions participated in glitches and coupling time-scales between various stellar components. The theoretical prediction for the time to the next glitch from the parameters of the previous one is found to be in qualitative agreement with the observed inter-glitch time-scales for the considered sample. Recoupling time-scales of the crustal superfluid are within the range of theoretical expectations and scale inversely with the spin-down rate of a pulsar. We also determined a braking index n = 2.63(30) for PSR J2229+6114 after glitch-induced contributions have been removed.

The close correlation observed between emission state and spin-down rate change of pulsars has many implications both for the magnetospheric physics and the neutron star interior. The middle-aged pulsar PSR J0738−4042, which had been observed to display variations in the pulse profile associated with its spin-down rate change due to external effects, is a remarkable example. In this study, based on the 12.5-yr combined public timing data from UTMOST and Parkes, we have detected a new emission-rotation correlation in PSR J0738−4042 concurrent with a glitch. A glitch that occurred at MJD 57359(5) (December 3, 2015) with Δν/ν ∼ 0.36(4) × 10⁻⁹ is the first glitch event observed in this pulsar and is probably the underlying cause of the emission-rotation correlation. Unlike the usual post-glitch behaviours, the braking torque on the pulsar has continued to increase over 1380 d, corresponding to a significant decrease in |$\ddot{\nu }$|⁠. As for changes in the pulse profile after the glitch, the relative amplitude of the leading component weakens drastically, while the middle component becomes stronger. A combined model of crustquake induced platelet movement and vortex creep response is invoked to account for this rare correlation. In this scenario, magnetospheric state-change is naturally linked to the pulsar-intrinsic processes that give rise to a glitch.

The long-term rotational evolution of the old, isolated pulsar, PSR B0950+08, is intriguing in that its spin-down rate displays sinusoidal-like oscillations due to alternating variations, both in magnitude and sign, of the second time derivative of the pulse frequency. We show that the large internal temperature to pinning energy ratio towards the base of the crust implied by the recent high surface temperature measurement of PSR B0950+08 leads to linear creep interaction between vortex lines and pinning sites to operate in this pulsar. Vortex lines assume a parabolic shape due to pinning to nuclear clusters and finite tension of vortices acts as a restoring force that tends to bring a vortex back to its straight shape. The resulting low-frequency oscillations of vortex lines combined with the time variable coupling between the internal superfluid components and the external pulsar braking torque give rise to an oscillatory spin-down rate. We apply this model to PSR B0950+08 observations for several external torque models. Our model has potential to constrain the radial extension of the closed magnetic field region in the outer core of neutron stars from the oscillation period of the spin-down rate.