Automobiles for our roadways are increasingly using advanced driver assistance systems. The adoption of such new technologies requires us to develop novel perception systems not only for accurately understanding the situational context of these vehicles, but also to infer the driver's awareness in differentiating between safe and critical situations. This manuscript focuses on the specific problem of inferring driver awareness in the context of attention analysis and hazardous incident activity. Even after the development of wearable and compact multi-modal bio-sensing systems in recent years, their application in driver awareness context has been scarcely explored. The capability of simultaneously recording different kinds of bio-sensing data in addition to traditionally employed computer vision systems provides exciting opportunities to explore the limitations of these sensor modalities. In this work, we explore the applications of three different bio-sensing modalities namely electroencephalogram (EEG), photoplethysmogram (PPG) and galvanic skin response (GSR) along with a camera-based vision system in driver awareness context. We assess the information from these sensors independently and together using both signal processing- and deep learning-based tools. We show that our methods outperform previously reported studies to classify driver attention and detecting hazardous/non-hazardous situations for short time scales of two seconds. We use EEG and vision data for high resolution temporal classification (two seconds) while additionally also employing PPG and GSR over longer time periods. We evaluate our methods by collecting user data on twelve subjects for two real-world driving datasets among which one is publicly available (KITTI dataset) while the other was collected by us (LISA dataset) with the vehicle being driven in an autonomous mode. This work presents an exhaustive evaluation of multiple sensor modalities on two different datasets for attention monitoring and hazardous events classification.