used to indicate obligation, duty, or correctness, typically when criticizing someone's actions

he should have been careful

I think we should trust our people more

you shouldn't have gone

used to indicate what is probable

£348 m should be enough to buy him out

the bus should arrive in a few minutes

(expressing the conditional mood) referring to a possible event or situation

if you should change your mind, I'll be at the hotel

should anyone arrive late, admission is likely to be refused

used in a clause with ‘that’ after a main clause describing feelings

it is astonishing that we should find violence here

used in a clause with ‘that’ expressing purpose

in order that training should be effective it must be planned systematically

(in the first person) expressing a polite request or acceptance

I should like some more, if I may

we should be grateful for your advice

(in the first person) expressing a conjecture or hope

he'll have a sore head, I should imagine

‘It won't happen again.’ ‘I should hope not.’

used to emphasize to a listener how striking an event is or was

you should have seen Marge's face