Volcanic seismicity is generated by a number of sources associated with the transport and eruption of magma and fluids, including explosions, fracturing, fault movement, and volcano uplift / subsidence. Spectral and statistical analyses, in particular, are fundamental for identifying and interpreting the processes behind such seismicity. The recording of this seismicity can generate enormous volumes of data that require robust, automated methods for processing. In this thesis, I explore the use of wavelet transform and deep learning methods for detecting and characterising seismicity relating to volcanic and magmatic processes. Application to examples of commonly observed volcano-seismic phenomena from a range of volcanic systems illustrates the comparative strengths of the continuous wavelet transform over the widely adopted short-time Fourier transform for broadband spectral analysis. Low-oscillation wavelets are then introduced and applied to concurrent short and ultra-long period (ULP) seismicity at the Santiaguito volcanic dome complex in Guatemala, revealing precursory ULP velocity signals ~ 10 min before explosions and the onset of dome inflation prior to eruption. Deep crustal seismicity in the Main Ethiopian Rift (MER) identified through an automated picking algorithm based on low-oscillation wavelets and statistical segmentation algorithms is the first observed in the MER; its ephemeral, swarm-like distribution suggests that high pore fluid pressure reactivates pre-existing faults in the lower crust, despite the crust's inferred ductile rheology at these depths (earthquake distribution mode between 28 and 32 km bsl). A highly efficient deep learning model to detect P- and S-wave phase arrivals is then developed to analyse volcanic earthquakes at Nabro volcano in Eritrea, a poorly studied volcano that had a large eruption in 2011. Transfer learning and a small training set of ~ 5,000 seismic waveforms (< 1,000 events) compiled using manually picked phase arrivals from a single month of data was used to train a model that detects 33,950 events from a 14-month seismic array deployed following the 2011 eruption, providing a substantial new earthquake catalogue for this volcano. Q attenuation for Nabro is determined through large systems of linearised spectral ratios; spectral decay and distribution modes for Q (45 < Q_P < 85 and 89 < Q_S < 185 across all stations) indicate a high degree of both intrinsic and scattering attenuation, with attenuation at stations closer to the volcano displaying greater frequency independence. Finally, spatial and statistical distributions of seismicity reveal a number of distinct processes around Nabro during this period, including stress transfer at neighbouring Mallahle volcano, fluid-fault interaction to the northeast of Nabro along the axis of the Nabro Volcanic Range, and the transport of fluids above and beneath an inferred aseismic magma storage region at 6 - 9 km bsl. The efficiency and robustness of the methods presented in this thesis make them ideally suited for fully-automated seismic event detection and characterisation for volcano monitoring purposes, even during significant periods of unrest and activity.