Passive acoustic mapping (PAM) is a novel method for monitoring ultrasound therapies by mapping sources of acoustic activity, and in most cases cavitation activity, using an array of detectors. Although the range of its applications is indicative of its great potential, clinical adoption is currently hindered by its limited spatial resolution and the inherent difficulty of distinguishing, at depth, between nonlinear signals arising from nonlinear propagation and those arising from processes such as cavitation. The objective of this thesis is to address this limitation, by improving both the detection of the signal-of-interest and the source localisation. An optimum data-adaptive array beamforming algorithm is proposed, Robust Beamforming by Linear Programming (RLPB), which exploits the higher-orderstatistics of the recorded signals, aiming at improving PAM source localisation. Both simulations and in vitro experimentation demonstrated improvement in PAM spatial resolution compared to a previously introduced algorithm, Robust Capon Beamformer. More specifically, under the in vitro conditions examined here, a 22% and 14% increase in the axial and transverse PAM resolution is respectively achieved. In terms of reliable signal-of-interest detection amongst interfering signals, a time-domain data-adaptive parametric model, Sum-of-Harmonics (SOH) model, is developed. This model enables accurate estimation of time-varying-amplitude narrowband components in the presence of broadband signals. Respectively, it can recover a weak broadband signal in the presence of a dominant narrowband component. Compared to conventional comb filtering, SOH model enables PAM of cavitation sources that better reflect their physical location and extent. PAM performance enhancement achieved by combining the proposed beamforming and filtering approaches is assessed in a context where spatial resolution really matters, namely for distinguishing between cavitation activity occurring inside a channel and perivascularly following cavitation-mediated extravasation. Adoption of the proposed method results in more accurate isolation of the broadband emissions from inertially cavitating sources, and more reliable localisation of these sources despite the long source-to-array distance has been observed. Such an improvement to the spatial accuracy of PAM paves the way towards its clinical translation, and in vivo experimentation is the next step for further validation of PAM in conjunction with the proposed methods under clinically relevant conditions.