I. INTRODUCTION  
A. Historical Perspective  
B. About Previous Surveys  
C. Paper Structure  

II. THE ACTIVE SLAM PROBLEM  
A. Problem Formulation  
B. Decoupling Active SLAM into Three Subproblems  

III. STAGE 1: IDENTIFICATION OF POTENTIAL ACTIONS  

IV. STAGE 2: UTILITY COMPUTATION  

V. STAGE 3: ACTION SELECTION AND EXECUTION  

VI. BELIEF-SPACE PLANNING AND CONTINUOUS-SPACE OPTIMIZATION  
A. Belief-Space Planning (BSP)  
B. Active SLAM as Optimal Control  

VII. DEEP-LEARNING-BASED APPROACHES  

VIII. MULTI-ROBOT ACTIVE SLAM  

IX. OPEN RESEARCH QUESTIONS  
A. Prediction Beyond Line-of-sight  
B. From Active SLAM to Active Spatial Perception  
C. Robust Online Belief Space Planning and Active SLAM  
D. Reasoning in Dynamic and Deformable Scenes  
E. Towards Meaningful and Autonomous Stopping Criteria  
F. Reproducible Research in Active SLAM  
G. Practical Applications  

X. CONCLUSIONS