We study the optimization of large-scale, real-time ridesharing systems and propose a modular design methodology, Component Algorithms for Ridesharing (CAR). We evaluate a diverse set of CARs (14 in total), focusing on the key algorithmic components of ridesharing. We take a multi-objective approach, evaluating 12 metrics related to global efficiency, complexity, passenger, driver, and platform incentives, in settings designed to closely resemble reality in every aspect, focusing on vehicles of capacity two. To the best of our knowledge, this is the largest and most comprehensive evaluation to date. We (i) identify CARs that perform well on global, passenger, driver or platform metrics, (ii) demonstrate that lightweight relocation schemes can significantly improve the Quality of Service by up to $50\%$, and (iii) highlight a practical, scalable, on-device CAR that works well across all metrics.