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	Abstract
1	Introduction
2	General Background
	2.1	Isolated systems
	2.2	The emergence of the current picture
	2.3	Asymptotically flat space-times
	2.4	Example: Minkowski space
	2.5	Going further
3	The Regular Conformal Field Equations
	3.1	General properties of the conformal field equations
	3.2	The reduction process for the conformal field equations
	3.3	Initial value problems
	3.4	Hyperboloidal initial data
	3.5	Space-like infinity
	3.6	Going further
4	Numerical Issues
	4.1	Why use the conformal method for numerical relativity?
	4.2	Construction of initial data
	4.3	Evolution equations
	4.4	Some numerical results
	4.5	Problems for future considerations
5	Acknowledgments
6	Appendix: Reduction of the Conformal Field Equations
7	Appendix: Conformal Rescalings and Curvature
	References
	Figures

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