Social media platforms have emerged as the widely accessed form of communication channel on the world wide web in the modern day. The first ever social networking website came into existence in the year 2002 and currently there are about 2.08 billion social media users around the globe. The participation of users within a social network can be considered as an act of sensing where they are interacting with the physical world and recording the corresponding observations in the form of texts, pictures, videos, etc. This phenomenon is termed as Social Sensing and motivates us to develop robust techniques which can estimate the physical state from the human observations.This dissertation addresses a set of problems related to detection and tracking of real-world events. The term ‘event’ refers to an entity that can be characterized by spatial and temporal properties. With the help of these properties we design novel mathematical models that help us with our goals. We first focus on a simple event detection technique using ‘Twitter’ as the source of information. The method described in this work allow us to perform detection in a completely language independent and unsupervised fashion. We next extend the event detection problem to a different type of social media, ‘Instagram’, which allows users to share pictorial information of nearby observations. With the availability of geotagged data we solve two different subproblems - the first one is to detect and geolocalize the instance of an event and the second one is to estimate the path taken by an event during its course. The next problem we look at is related to improving the quality of event localization with the help of text and metadata information. Twitter, in general, has less volume of geotagged data available in comparison to Instagram, which demands us to design methods that explore the supplementary information available from the detected events. Finally, we take a look at both the social networks at the same time in order to utilize the complementary advantages and perform better than the methods designed for the individual networks.