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We address the controversial issue of traffic flow modeling, whether first-order, second-order, or other traffic models are best supported by empirical facts and theoretical considerations. This is done by a critical discussion of the pros and cons of the different theoretical approaches and by the analysis of a large set of empirical data with new evaluation techniques. Specifically, we investigate characteristic properties of the congested traffic states on a 30-km-long stretch of the German freeway A5 near Frankfurt/Main. Among the approximately 245 breakdowns of traffic flow at several different bottlenecks in 165 days, we have identified five different kinds of spatiotemporal congestion patterns and their combinations. Based on an "adaptive smoothing method" for the visualization of detector data, we also discuss particular features of breakdowns, such as signs of unstable traffic flow and the "boomerang effect," which often seems to be caused by overtaking maneuvers of trucks. Controversial issues such as "synchronized flow" or stop-and-go waves are addressed as well. Our empirical results are compared with the implications of different theoretical concepts such as first-order traffic models and the phase diagram of congested traffic states predicted by some second-order models and the nonlocal, gas-kinetic based traffic model (GKT model). For a correct understanding of empirical observations such as the "general pattern," it is important to consider particularities such as the fact that off-ramps can act as bottlenecks, when activated by downstream on-ramp bottlenecks. As sequences of off- and on-ramps generate different congestion patterns than single on-ramps, they must be treated as interconnected bottlenecks. Furthermore, our empirical results question Kerner's three-phase theory. [ABSTRACT FROM AUTHOR]