Transients and magnetohydrodynamic (MHD) waves are ubiquitous in the solar atmosphere, which play a crucial role in the energy and mass transport. Therefore, understanding of the drivers and physical properties of these phenomena is at the forefront of solar physics research. Under the framework of the topic of my Ph.D. thesis, some transients at diverse spatio-temporal scales, as well as the role of MHD waves and pulses in these transients have been investigated. In the first chapter, I present an updated overview, reviewing comprehensively the physics and recent developments in various transients and MHD waves, and finally outline the plan of my various thesis chapters. In the second chapter, I report the estimated plasma properties of an active region surge using SDO/AIA, HMI observations, and conclude by our model that thermal pulse in the lower solar atmosphere can trigger the observed surge. The third chapter describes that the internal reconnection in the kinked small-scale magnetic fluxtube evolving at the polar cap of the Sun, triggers a macrospicule and associated coronal jet. The stringent 2-D MHD model depicts that the small-scale reconnection originates a velocity pulse, which steepens in the polar corona and generates the observed macrospicule and jet like plasma perturbations. Another case study of Alfven wave driven polar coronal jet, using Hinode/EIS spectral observations, is also presented in the same chapter. It is found that the reconnection in the 2-D vertical current sheet in polar corona triggers Alfven waves and related vertical plasma flows, which constitute the observed jet-like motion. In the fourth chapter, I investigate the source regions of the plasma flows and signature of the Alfvén waves in the quiet-Sun (QS) and coronal holes (CH) using the spectroscopic observations of Hinode/EIS, which have significant physical implications on the localized coronal heating and mass transport to the nascent fast solar wind. I have finally reported the first observational evidence of sausage-pinch magnetohydrodynamic (MHD) instability in a large-scale eruptive prominence tube in the fifth chapter, and discuss its physical significance in the solar coronal eruptions and magnetized plasma. In conclusion, the original research works as described in various chapters of my thesis, shed new light to the physical properties and drivers (MHD waves, pulses, instabilities) of the solar transients at diverse spatio-temporal scales.