In this work, functionalised microbubbles are investigated as a new platform for acoustic biosensing. In medical ultrasound, encapsulated microbubbles (MBs) are injected into the body to enhance contrast between blood and surrounding tissue. Microbubbles are not only good ultrasound scatterers: when placed in an ultrasound field, they act as non-linear resonators, generating harmonic energies in the scattered acoustic signal, and this can be further exploited for biosensing. Analytical models and finite element method (FEM) simulations for the interaction between high frequency (1-300 MHz) acoustic waves and encapsulated microbubbles, show that an incident acoustic wave can set a microbubble into mechanical resonance. The resonant frequency is strongly dependent on the shell properties (thickness, elasticity, viscosity, $etc.$), and it is affected by a layer of material attaching to its surface. Existing analytical models in the literature cannot predict the change in microbubble resonance when the material properties of the added layer differ to those of the shell. A new model describing the dynamics of encapsulated and functionalised microbubbles is developed and validated in this thesis. The new Rayleigh-Plesset-like equation accounts for the interaction between the functionalisation layer and the encapsulating shell. Complementary FEM simulations predict that the addition of a 100 nm-layer with a low shear modulus, mimicking the attachment of a biological material, to 100 nm-shell thickness silica microbubbles with radii in the range 1.96-2.33 $\mu$m, lowers the resonant frequencies by $\sim$ 10 to 6 MHz. Nearly monodispersed silica-organosilane-silica microbubbles are fabricated with radii in this range, using a core-shell technique. The synthesis method enables excellent control of size distribution and shell thickness of the microbubbles, which can be tailored for maximum resonance in a desired frequency range. An acoustic system has been designed and constructed to retrieve the high-frequency response of the microbubbles, remotely measure the shift in microbubble resonant frequencies upon attachment and hence detect the presence of biological molecules in a fluid. Onset of microbubble resonance on different silica-organosilane-silica microbubble populations has been detected through measurement of frequency-dependent acoustic scattering spectra in the range 20-30 MHz. The experimental observations are in good agreement with theoretical predictions. Locations of the peaks on the spectra are compatible with resonance of microbubble populations having different cavity radius size and fixed shell thickness. The simulations and experimental results indicate that bioanalyte binding events, taking place on the surface of a microbubble, generate measurable shifts in resonant frequency, detectable from near-field and far-field acoustic scattering. This sensing strategy overcomes the classic biosensing paradigm through a technology in which functionalisation of a fixed surface is not required, enabling acoustic $in-vivo$ biosensing. In view of the translation of the technology into clinical applications, a concept for a microelectromechanical microbubble biosensor is explored. The proposed sensor is composed of a microfluidic channel integrated with a new type of acoustic waveguide sensor, utilizing surface acoustic wave (SAW) coupled resonators. The detection of particles and microbubbles, and the characterisation of liquid properties, are based on multiple mode conversion and coupling of SAWs at solid-liquid interfaces. Functionalised microbubbles are injected through the sensor and changes in microbubble acoustic properties, associated with the binding of complementary biological molecules, will be measured. With no need of immobilisation of receptors on fixed surfaces the new sensor will be more amenable for $in-vivo$ biosensing than existing acoustic wave resonators.