Recently, there has been an increasing focus on various biological and physical systems known as "active matter". Examples of such systems range from individual units, such as motile cells or artificial self-propelled particles, to large systems of interacting active particles or individuals. The emergence of large-scale collective motion, as exhibited by flocks of birds or bacterial colonies, is just one prominent and fascinating example of self-organization in active matter systems. In this work, we discuss different individual-based models of active matter using the concept of active Brownian motion. The first part of this work explores the dynamical behavior of single active particles with a particular emphasis on the impact of so-called active fluctuations. The second part extends the scope of this study to interacting active Brownian particles and their collective behavior. First, a systematic derivation of kinetic equations for active Brownian particles with velocity alignment is presented. Further on, motivated by recent biological observations, a new type of "escape-pursuit" model of collective motion is introduced and successfully employed in modeling collective locust behavior.