How to extend the chart of nuclides?

In the past 85 years the number of known nuclides increased by more than a factor of ten, resulting in 4000 presently known isotopes of 118 elements. This considerable progress we owe to the discovery of new reaction types along with the development of powerful accelerators and experimental techniques for separation and identification of reaction products. Model predictions indicate that still about 4000 further nuclides are waiting for their discovery. The vastest unexplored territory is located on the neutron-rich side in the upper half of the chart of nuclides and hides the answers to some of the most fundamental questions of nuclear physics like the limits of nuclear stability, element synthesis in the universe or stellar evolution. The access to these nuclei is presently limited by available beam intensities and/or the lack of appropriate methods for their production and identification. The latter concerns particularly new neutron-rich isotopes of transuranium and superheavy elements. To extend this area, the hope is presently based on multinucleon transfer reactions and on the application of fusion reactions with radioactive ion beams. But how promising are these approaches? Based on a survey of present-day knowledge, we will treat the questions where we currently are on our journey towards new territory on the chart of nuclides, how the chances are to gain new territory in the future and which challenges we will have to face.