The rapid emergence and growth of transportation network companies (TNCs) such as Uber, Lyft, and Didi Chuxing, operating app-based on-demand ride-sourcing services, has led to a debate over the role of TNCs in the urban transport system. The growth of the ride-sourcing business has brought significant challenges for planners, engineers, and policy makers, due to the magnitude and uncertainty of its impacts. This dissertation focuses on several aspects of on-demand mobility, mostly related to equity and behavior, and answers some of the most debated questions about ride-sourcing to provide important evidence for engineers, planners and policy makers on future ride-sourcing related policy decisions.The equity analysis investigates the effects of ride-sourcing fare changes to passengers with different socio-economic backgrounds. Using a large GPS-based travel dataset from 2015 in Shanghai, I conducted panel analysis of how ride-sourcing demand was related to average property value, as a proxy for socioeconomic status, measured at small spatial scale at trip origins and destinations. I modeled the ride-sourcing demand (for pick-ups and drop-offs separately) as a product of several spatial and temporal characteristics, using a negative binomial regression with fixed effects whose functional form is appropriate for dispersed count data. The results imply that a decrease in ride-sourcing fares would likely benefit middle to high income travelers more than low-income travelers, by making ride-sourcing an economically competitive mode for those groups. Usage is much higher in neighborhoods with higher property values when fares are lower. At the same time, however, there is still significant though lower use of ride-sourcing in lower-income neighborhoods, and usage in those locations is less responsive to the fare. I conclude that ride-sourcing policy which results in fare increases would likely to pose a substantial burden for lower-income travelers, although the number of such lower income travelers may be small compared to the number of middle-to-high income travelers.The behavioral analysis focuses on three questions: (1) Is parking supply associated with lower ride-sourcing demand? (2) Does better transit access reduce or increase the use of ride-hailing? and (3) Does higher congestion affect ride-sourcing demand? I modeled the ride-sourcing demand (for pick-ups and drop-offs separately) using a generalized additive mixed model (GAMM). The results suggest that first, parking would not necessarily reduce the demand for ride-sourcing unless the parking supply is large enough. Second, whether ride-sourcing compete or complement bus transit depends on the coverage of bus services: they tended to compete when the density of bus stops is high, and complement each other when there are fewer bus stops. Third, ride-sourcing demand was positively correlated with congestion, except that when congestion is severe, there were fewer pick-ups. In addition to the panel study, I used Google Map API to figure out if each actual ride-sourcing trip has transit alternative. I found that over 90% of the actual ride-sourcing trips have transit alternatives, but transit compete poorly with ride-sourcing because of much longer travel time, need multiple transfer and longer walking. Finally, I discussed policy implication based on these empirical findings.