1 Introduction

2 Simplicity and Complexity
2.1 Exact Values for Ordinary Graphs
2.2 Characterizations of Trees
2.3 Complexity for General Graphs

3 Upper Bounds
3.1 Most Basic Upper Bounds
3.2 Bounds Implied by Connectivity
3.3 Bounds Implied by Degree Sequence
3.4 Bounds in γ-critical Graphs
3.5 Bounds Implied by Domination
3.6 Two Conjectures

4 Lower Bounds

5 Results on Graphs-operations
5.1 Cartesian Product Graphs
5.2 Block Graphs and Cactus Graphs

6 Results on Planar Graphs
6.1 Conjecture on the Bondage Number
6.2 Bounds Implied by Maximum Degree
6.3 Bounds Implied by Degree-conditions
6.4 Bounds Implied by Girth-conditions
6.5 Comments on the Conjectures
6.6 Minimum Counterexamples to the Conjectures

7 Results on Crossing Number Restraints
7.1 General Methods
7.2 Carlson and Develin’s Methods

8 Other Types of Bondage Numbers
8.1 Restrained Bondage Numbers
8.2 Total Bondage Numbers
8.3 Paired Bondage Numbers
8.4 Independence Bondage Numbers

9 Generalized Types of Bondage Numbers
9.1 p-Bondage Numbers
9.2 Distance Bondage Numbers
9.3 Fractional Bondage Numbers
9.4 Roman Bondage Numbers
9.5 Remarks and Comments

10 Results on Digraphs
10.1 Upper Bounds for General Digraphs
10.2 Results for Some Special Digraphs

11 Efficient Dominating Sets
11.1 Results for General Graphs
11.2 Results for Cayley Graphs
11.3 Comments