Emotions are complicated psycho-physiological processes that are related to numerous external and internal changes in the body. They play an essential role in human-human interaction and can be important for human-machine interfaces. Automatically recognizing emotions in conversation could be applied in many application domains like health-care, education, social interactions, entertainment, and more. Facial expressions, speech, and body gestures are primary cues that have been widely used for recognizing emotions in conversation. However, these cues can be ineffective as they cannot reveal underlying emotions when people involuntarily or deliberately conceal their emotions. Researchers have shown that analyzing brain activity and physiological signals can lead to more reliable emotion recognition since they generally cannot be controlled. However, these body responses in emotional situations have been rarely explored in interactive tasks like conversations. This paper explores and discusses the performance and challenges of using brain activity and other physiological signals in recognizing emotions in a face-to-face conversation. We present an experimental setup for stimulating spontaneous emotions using a face-to-face conversation and creating a dataset of the brain and physiological activity. We then describe our analysis strategies for recognizing emotions using Electroencephalography (EEG), Photoplethysmography (PPG), and Galvanic Skin Response (GSR) signals in subject-dependent and subject-independent approaches. Finally, we describe new directions for future research in conversational emotion recognition and the limitations and challenges of our approach.