We review several important experimental and theoretical developments
that during the past decade have revived interest in the stability pro
perties of the heaviest elements. On the experimental side two accompl
ishments stand out. One is the extension of the known elements to 107N
s, 108Hs and 109Mt. The other is the collection of an extensive body o
f data on the transition between asymmetric and symmetric fission in t
he region close to proton number Z = 2 x 50 and neutron number N = 2 x
82. On the theoretical side it has become clear that some models that
appropriately account for the most important nuclear-structure aspect
s are sufficiently reliable for meaningful applications to new regions
of nuclei and to studies of new phenomena. We discuss here in particu
lar the importance of a 'few-parameter approach' and of solving a Schr
oedinger equation for accurately obtaining microscopic effects. We sho
w how such models now more reliably than earlier describe the stabilit
y properties of the heaviest elements when the following importnat poi
nts are treated carefully. In fission studies very precise shape speci
fications are necessary in the saddle-point region and beyond. Coulomb
redistribution effects and higher-multipole effects are important for
determining the ground-state masses. We review how consideration of t
hese effects has influenced theoretical work in the last decade and pr
esent some current results on alpha-decay, beta-decay and fission prop
erties in the heaviest region.