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let me first start with what this talk will not be :    * an introduction to supersymmetry .
first of all you are all experts in the field , and second we just attended an excellent introductory presentation@xcite ; * a discussion of the cosmological aspects , mostly due to my inability ; * a comprehensive review because of the limited amount of time available .
this discussion will rather focus on :    * the lep legacy , with minimal experimental details , because the lep results often remain the most constraining at this point ; * recent results from the run ii of the tevatron , which is curently the most powerful collider in operation . at the tevatron ,
proton - antiproton collisions take place at a center - of - mass energy of 1.96  tev , and the instantaneous luminosity recently reached the @xmath0@xmath1s@xmath2 level .
the frameworks in which these results will be presented are :    * most of the time `` standard susy '' .
this means the mssm , often with some generic unification constraints ( essentially for slepton or gaugino susy - breaking masses ) at the scale of grand unification ( gut ) , and with the assumption that the lightest supersymmetric particle ( lsp ) is the lightest neutralino @xmath3 .
occasionnally , the model considered will be even more constrained in the form of minimal supergravity ( msugra ) ; * in a few instances gauge mediated supersymmetry breaking ( gmsb ) , which offers clean and simple signatures , in its minimal version ; * with r - parity conservation .
again , this is mostly due to lack of time in view of the large number of equally acceptable scenarios , and also partly because of a personal prejudice having to do with the absence of dark matter in r - parity violating models .
( here i have to seek forgiveness from my hera colleagues . )    at lep , all supersymmetric particles , except for the gluinos , are produced in a rather democratic fashion via electroweak interactions , up to mass effects . since
pair production of the lsp is not directly detectable , the search is naturally directed towards the next - to - lightest supersymmetric particles ( nlsp s ) .
the results can often be presented in a model independent , or at least moderately dependent , way .
results from various channels can furthermore be combined within some specific theoretical framework to derive additional constraints , of which the most celebrated one is the lsp - mass lower limit .    at the tevatron ,
colored particles ( i.e. , squarks and gluinos ) are expected to be produced with large cross sections via strong interactions .
the resulting final states consisting mostly of jets and missing transverse energy however suffer from large backgrounds from standard multijet production .
the electroweak production of charginos and neutralinos has a much lower cross section , but clean final states such as trileptons and missing transverse energy are considerably easier to discriminate from standard model backgrounds .
finally , in contrast to the situation at lep , a model independent presentation of the results is usually unavailable because it is highly unpractical to provide one which would be both transparent and meaningful .
all limits ( unfortunately ... ) quoted in the following are given at 95% confidence level .
because this is probably the simplest channel , both theoretically and experimentally , among those which have been analysed at lep , let us begin with the search for smuon pair production , which proceeds only through @xmath4 exchange in the @xmath5-channel .
it is assumed that it is the supersymmetric partner @xmath6 of the right - handed muon which is the lighter of the two smuons , an assumption which is valid in models involving the unification of susy - breaking masses and which is conservative in terms of production cross section .
the only parameter which is needed to calculate this cross section is the smuon mass . if the smuon is furthermore assumed to be the nlsp , the only decay channel available is @xmath7 , and the only additional parameter involved is the lsp mass @xmath8 .
the final state consists in a pair of acoplanar muons , and the main background , from @xmath9 , is well under control .
the search result obtained by the four lep experiments combined is shown in fig .  [
smuonstop](left )  @xcite ; the gap along the diagonal is due to the softness of the muons when the @xmath10 
@xmath3 mass difference is very small . with the additional condition of gaugino mass unification
, the assumption that the smuon is the nlsp can be relaxed , and the effect of cascade decays such as @xmath11 with @xmath12 can be incorporated .
these cascade decays occur only at small values of @xmath8 , for which the smuon mass limit of almost 100  gev is slightly degraded .    [ cols="^,^ " , ]     the question can be raised of the relevance of the tevatron searches for squarks and gluinos .
indeed , if gaugino mass unification is assumed , as it is the case in msugra , the lep limits on charginos translate into gluino mass limits well beyond those within the tevatron reach .
similarly , if slepton and squark mass unification is assumed , the lep limits on selectrons are more restrictive than those on squark masses from the tevatron .
the cdf and dcollaborations should therefore be encouraged to present their results within frameworks other than msugra .
for instance , in susy - gut models where susy breaking is induced by an f - term which is a * 75 * of su(5 ) , rather than by a singlet , the @xmath13 ratio is of order unity , in which case lep results do not constrain gluino masses above 105  gev or so .
string inspired models can also lead to similar gaugino mass hierarchies .
before concluding , i want to quote a result which is a bit off the main track , but still relevant for supersymmetry .
the cdf and d  collaborations have searched for the rare decay @xmath14 which is expected to be at the 3.5  10@xmath15 level in the standard model , but may be enhanced by a factor of @xmath16 , i.e. , by as much as three orders of magnitude , in supersymmetry . at the time this talk was given , the cdf collaboration had quoted a limit of 7.5  10@xmath17  @xcite , improving substantially over the previous best limit and probing relevant new territory , while the d  collaboration had not yet `` opened the box . ''
has been set  @xcite ]    as of today , the main constraints on supersymmetry obtained at accelerators remain those established by lep . if fine tuned parameter configurations are discarded , limits of the order of 100  gev are set on slepton and chargino masses , and the mass of the lightest supersymmetric particle has to exceed 47  gev in the mssm with slepton , squark and gaugino mass unification .
the tevatron is however already providing relevant results . in the framework of gauge
mediated supersymmetry , a lower limit of 108 gev has been set on the mass of a neutralino nlsp .
trilepton searches should lead to new constraints on minimal supergravity in the near future .
squark and gluino searches are well underway , although an adequate interpretation of the results is still lacking . with the continuously improving performance of the tevatron
, the coming years can be expected to provide an exciting harvest of new results .
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the cdf exotics group : + http://www-cdf.fnal.gov/physics/exotic/exotic.html d  new phenomena results : + http://www-d0.fnal.gov/run2physics/www/results/np/np.htm d  b physics results : + http://www-d0.fnal.gov/run2physics/www/results/b/b.htm
searches for supersymmetric particles at lep are first reviewed , with some emphasis on the mass limit for the lightest neutralino . 
 the framework is the mssm with r - parity conservation , with brief excursions towards msugra and gmsb . 
 next , recent results obtained in the run ii of the tevatron are presented .