Chapter 1 Introduction 1.1 Research Significance 1.2 Current Research Status and Development Trends at Home and Abroad 1.3 Theoretical Model of Active Brownian Particles 1.3.1 Soft Matter and Active Matter 1.3.2 Passive Brownian Motion 1.3.3 Active Brownian Motion 1.3.4 Run-and-Tumble Motion 1.3.5 Chiral Active Brownian Motion 1.3.6 Gaussian Noise Reorientation Model 1.3.7 Complex Models 1.4 Basic Techniques 1.5 Summary Chapter 2 Directed Transport of Mobile Obstacles Driven by Active Particles 2.1 Introduction 2.2 Transport of the Moving Obstacle Driven by Alignment Active Particles 2.2.1 Model and Methods 2.2.2 Results and Discussion 2.3 Transport of the Obstacle Lattice with Topographical Gradients Driven by Chiral Active Particles 2.3.1 Model and Methods 2.3.2 Results and Discussion 2.4 Conclusions Chapter 3 Directed Transport of Inertial Active Particles in Complex Environments 3.1 Introduction 3.2 Rectification of Chiral Attractive Active Particles under Inertial Effects in Transverse Temperature Difference 3.2.1 Model and Methods 3.2.2 Results and Discussion 3.3 Transport and Absolute Negative Mobility of Inertial Brownian Particles Induced by Harmonic Force in Steady Laminar Flows 3.3.1 Model and Methods 3.3.2 Results and Discussion 3.4 Conclusions Chapter 4 Directed Transport of Deformable Particles under Different Potential Landscapes 4.1 Introduction 4.2 Absolute Negative Mobility of an Inertial Deformable Particle under Steady Laminar Flows 4.2.1 Model and Methods 4.2.2 Results and Discussion 4.3 Directed Transport of Multiple Deformable Particles in Time-Oscillating Potentials 4.3.1 Model and Methods 4.3.2 Results and Discussion 4.4 Conclusions Chapter 5 Mixing and Demixing of Binary Mixtures of Active and Passive Rodlike Particles 5.1 Introduction 5.2 Model and Methods 5.3 Results and Discussion 5.3.1 Reflective Boundary Conditions 5.3.2 Periodic Boundary Conditions 5.3.3 Additional Results 5.4 Conclusions Chapter 6 Conclusions and Outlook 6.1 Conclusions