1 Introduction  
2 Online Matching and Ad Allocation  
2.1 Breaking the $1/2$ Barrier in Longstanding Open Problems  
2.2 Stochastic Rewards and Oblivious Budget  
3 Beyond Online Bipartite Matching and Ad Allocation  
3.1 Fully Online Model: Vertices with Arrivals and Deadlines  
3.2 General Vertex Arrival  
3.3 Edge Arrivals  
3.4 Reusable Resources  
4 Stochastic Models: Secretaries, Prophets, and Philosophers  
4.1 Secretary Problems  
4.2 Prophet Inequalities  
4.3 Philosopher Inequalities  
5 Overarching Techniques  
5.1 Primal-Dual Algorithms  
5.2 Randomized Rounding and Contention Resolution Schemes  
5.3 Online Contention Resolution Schemes  
5.4 Online Rounding: Online Correlated Selection