This chapter discussed some of the algorithmic choices one encounters when designing an IVHM system. While it would be generally desirable to be able to pick a particular set of algorithms for a particular problem, the reality is a bit more complex. Depending on the budget, the performance requirements, the computational constraints, sensor availability, access to historical data, operational and environmental conditions, robustness to changing system configurations, algorithm maintenance needs, etc., no one algorithm will perform best in all situations. Indeed, it is necessary to evaluate these constraints during the algorithm design process and determine the best choice on a case-by-case analysis. The trade-offs between different choices are very real, and sometimes no solution can be found, which means that some of the constraints have to be relaxed. The simplest solution is generally preferred over a more complex one, but it is also important to consider that there is no free lunch. Finally, any health management solution also has to undergo verification and validation (V&V) and, in some cases, certification. Some of these issues are topics of other chapters in this book.