Active matter systems operate far from equilibrium, with individual components consuming energy from their environment or internal sources, leading to self-propulsion and the breaking of time-reversal symmetry. These systems are prevalent in nature across various scales, inspiring the design of artificial active matter.  Self-propulsion in active matter often involves a breakdown of parity in the heading direction, which can undergo continuous (as in active Brownian particles or active colloids) or discrete reorientation (as in run-and-tumble particles or bacteria). Additionally, the left-right parity symmetry around the heading direction can be disrupted, leading to chirality, where agents turn in a direction dictated by the broken symmetry during self-propulsion. Chirality is observed in various natural systems, such as bacteria near interfaces and sperm cells swimming in helical patterns, as well as in synthetic systems like colloidal microswimmers with broken chiral symmetry and motile droplets. In this talk, I will discuss a Laplace transform-based method applied to the Fokker-Planck equation, providing a consistent approach for calculating all dynamical moments of a single chiral active Brownian particle (cABP) in both two and three dimensions. This unified approach reproduces known results and provides closed-form analytic expressions for various properties, including the mean squared displacement (MSD) components along and perpendicular to the heading direction, and the fourth moment of displacement. We also derive explicit expressions for the long- and short-time scalings of the excess kurtosis in both dimensions, which exhibits oscillations with multiple zero crossings at intermediate time scales. Furthermore, we extend this method to study cABP in a harmonic trap, precisely calculating the steady-state kurtosis depending on activity, chirality, and trap stiffness, revealing four distinct regimes: Rotating Active (RA), Rotating Passive (RP), Nonrotating Active (NRA), and Nonrotating Passive (NRP). Finally, we examine the effect of inertia on the dynamics of a cABP in two dimensions.