Hi Bill,
The way I understand it is that you will still need to go through the motions of taxing your vehicle(s) but as DVLA records will hold all the details on computer, which will be readily available to the authorities, there will be no need to physically display the tax disc.
Is your 59 on SORN? If so, you won't get a reminder because it will now remain SORNED until you sell the machine or tax it, unlike previously when you had to SORN the machine on an annual basis. If the actual tax has expired I would guess that the reminder has gone walkabout in the postal system and you should either tax it or SORN it asap.
The other thing to note that as of October, if you buy a vehicle that is taxed, the tax doesn't come with that vehicle and you will need to tax it yourself. On the other hand, if you sell a vehicle that you have paid road fund duty (tax) on, the duty won't be transferred to the new owner and DVLA will send you an automatic refund of the outstanding amount.
Apart from these points there are probably other changes to the new system that we in the UK will need to familiarise ourselves with.
Hope this helps,
Beezageezauk.