In this thesis, acoustofluidic platforms have been developed to manipulate microparticles inside a microfluidic channel and a sessile droplet. Acoustofluidic devices utilized for this purpose are based on surface acoustic waves and Lamb waves. Separation of two different sized particles, with diameter difference less than one micrometer, is realized by the high frequency travelling waves. Another travelling waves-based device is further used to demonstrate tri-particle separation where waves originate from two opposite locations of the microchannel and form uniquely observed microchannel anechoic corners within the channel. The acoustofluidic platform is used to perform size-independent separation of particles as well. Similarly, particles manipulation and separation have been demonstrated within sessile droplets. The fundamental principles behind the efficient manipulation of microparticles are the direct acoustic radiation forces by the travelling and standing acoustic waves which are combined with the acoustic streaming flow based drag force to obtain desired results. The dimensions of the fluidic domain carrying the particles are important parameters along with the frequency of the incident waves and the diameter of the particles. Theoretical estimation of the acoustic radiation force provides the necessary framework to choose appropriate experimental conditions for a particular application.