In conversational settings, individuals exhibit unique behaviors, rendering a one-size-fits-all approach insufficient for generating responses by dialogue agents. Although past studies have aimed to create personalized dialogue agents using speaker persona information, they have relied on the assumption that the speaker's persona is already provided. However, this assumption is not always valid, especially when it comes to chatbots utilized in industries like banking, hotel reservations, and airline bookings. This research paper aims to fill this gap by exploring the task of Speaker Profiling in Conversations (SPC). The primary objective of SPC is to produce a summary of persona characteristics for each individual speaker present in a dialogue. To accomplish this, we have divided the task into three subtasks: persona discovery, persona-type identification, and persona-value extraction. Given a dialogue, the first subtask aims to identify all utterances that contain persona information. Subsequently, the second task evaluates these utterances to identify the type of persona information they contain, while the third subtask identifies the specific persona values for each identified type. To address the task of SPC, we have curated a new dataset named SPICE, which comes with specific labels. We have evaluated various baselines on this dataset and benchmarked it with a new neural model, SPOT, which we introduce in this paper. Furthermore, we present a comprehensive analysis of SPOT, examining the limitations of individual modules both quantitatively and qualitatively.