Microtubules (MTs) are important linear protein filaments which participate in many intracellular physiological processes and provide mechanical support against external compression. The kinetics and mechanics of MTs change rather distinctively in different environment. It is therefore important to examine the interaction of MTs with the environment they are in, for a better understanding of how intracellular physiological phenomena are achieved. In this thesis, I first examine the effect of the quenched-disordered intracellular cytoskeleton network on the critical buckling of MTs. I apply the replica technique and find that the disorder reduces the critical buckling force, and the increase in disorder strength acts as the trigger of the switch from the first- and second-order buckling, in analogy to phase transitions. I then consider a system of fiber-crumbling inside cell aggregate, as an example to show the effect of the external environment on the ‘post-buckling’ pattern. I fit the experimental helix pitch size and radius with a helical buckling theory in an elastic medium, to extract the collective force generated by the cell aggregate on the crumbled fiber and the elasticity of this aggregate – this force value is from a few hundreds of nN to a few μN, and the estimated elastic modulus is weak and below 200 Pascals. In kinetics, MTs in cells experience a repeated pattern of length growth and shrinkage, where free tubulin concentration in solution is a key environmental factor determining the average time of growth and shrinkage. I consider the effect of the MT structural change induced by hydrolysis of GTP-tubulins on the average MT growth time before shrinkage, as a function of tubulin concentration, using a mean-first-passage-time (MFPT) method. The results are comparable with experiment in the low-medium concentration regime, making it a potential MT catastrophe mechanism in contrast with the popular GTP-cap models, where the structural information is over-simplified. I further investigate a kinetic process of dissociating MTs being ‘rescued’ into regrowth, by GTP-tubulin islands produced via random hydrolysis along the filament. I formulate this kinetic problem as a particle passing through partially-adsorbing traps, with the MFPT method. By comparing the theoretical averaged MT rescue site with experiment, I discover that only the scenario of slow hydrolysis and high tubulin concentration, with a large rescue reaction timescale, has a chance to match with the experimental mean rescue site. Thus, I suspect that GTP-islands created solely by random hydrolysis cannot fully explain the observed MT rescue kinetics.