The synthesis of superheavy elements is now a hot topic in nuclear physics. Alpha-decay and spontaneous fission are two main
decay modes in heavy and superheavy regions. Theoretical studies on alpha radioactivity and spontaneous fission can provide
useful information for experiments. We investigate the alpha-decay and spontaneous fission of heavy and superheavy nuclei
with different models. This includes the alpha-decay energies, alpha decay half-lives, and half-lives of spontaneous fission.
The theoretical alpha-decay half-lives are in good agreement with experimental ones. The calculated half-lives of spontaneous
fission are in reasonable agreement with present data. The properties of unknown nuclei are predicted.