Results from new observations of pulsars using the Ooty Radio Telescope (ORT) are used for investigating the structure of the Local Interstellar Medium (LISM). The observations show anomalous scintillation effects towards several nearby pulsars, and these are modeled in terms of large-scale spatial inhomogeneities in the distribution of plasma density fluctuations in the LISM. A 3-component model, where the Solar neighbourhood is surrounded by a shell of enhanced plasma turbulence, is proposed for the LISM. The inferred scattering structure is strikingly similar to the Local Bubble. Further, analysis based on recent scintillation measurements show evidence for enhanced scattering towards pulsars located in the general direction of the Loop I Superbubble. The model for the LISM has been further extended by incorporating the scattering due to turbulent plasma associated with Loop I.