Filtering and smoothing methods are used to produce an accurate estimate of the state of a time‎-varying system based on multiple observational inputs ‎(‎data‎)‎‎.‎ Interest in these methods has exploded in recent years‎,‎ with numerous applications emerging in fields such as navigation‎,‎ aerospace engineering‎,‎ telecommunications and medicine‎.‎ This compact‎,‎ informal introduction for graduate students and advanced undergraduates presents the current state‎-of‎-the‎-art filtering and smoothing methods in a unified Bayesian framework‎.‎ Readers learn what non‎-linear Kalman filters and particle filters are‎,‎ how they are related‎,‎ and their relative advantages and disadvantages‎.‎ They also discover how state‎-of‎-the‎-art Bayesian parameter estimation methods can be combined with state‎-of‎-the‎-art filtering and smoothing algorithms