As we contemplate the future roadmap, here is information surrounding the support of Direct Debit for Recurring and how our key providers support the capability:
INGENICO
Ingenico keeps track of a mandate being agreed to and the date & location. For example as outlined here under "sepaDirectDebit.mandate.mandateApproval":
https://epayments-api.developer-ingenico.com/s2sapi/v1/en_US/java/tokens/create.html?paymentPlatform=GLOBALCOLLECT#tokens-create-payload
For Direct Debit, Ingenico supportsthe networks in the UK ("BACS"), Europe ("SEPA") and the US ("ACH").
Here's our summary info on each:
https://epayments.developer-ingenico.com/payment-product/ach/overview/
https://epayments.developer-ingenico.com/payment-product/direct-debit-uk/overview/
https://epayments.developer-ingenico.com/payment-product/sepa-direct-debit/overview/

ADYEN
Integration documentation here:
https://docs.adyen.com/payment-methods/sepa-direct-debit

Relevant thread on the mechanics of DD here:
Thanks for your reply! Our main interest is to use SEPA as a recurring donation option.
Questions in line:

On Mon, Aug 13, 2018 at 11:21 AM, Joey Battja <joey.battja@adyen.com> wrote:
Hi both,

Regarding e-signatures: there are several services in Europe that offer an interface with the shopper’s bank to register an e-mandate; during this flow the shopper is redirected to his bank and can authorise his/her consent by doing a bank authentication.
Unfortunately there is no pan-European service, but only a few local ones and in most countries this is actually still a paper process. Moreover, even when having registered an e-mandate, the shopper can still chargeback the purchase until 8 weeks after payment date from the online banking interface without giving any reason nor are there any defence procedures in place.

We do not accept these type of e-mandate services. And they are honestly not very popular (as a Dutch person, I’ve not even once had to register a mandate this way, while this service does exist in NL for a few years already).

What we do offer as a (better) alternative is:
1.) collecting IBAN’s via an online banking payment method, like iDEAL in NL, Sofort in DE, EPS in AT, Bancontact in BE, etc. and store those IBANs as tokens to be used for any subsequent SEPA Direct Debits.
The benefit of this is that we’re using a payment methods shoppers are used to (better conversion) to securely verify whether the shopper owns (or at least has access to) the account.

Would the flow be different in each country (the same as the regular IDEAL, Sofort, etc) versus a unique SEPA DD flow?
Yes this flow in which we would collect the bank account would be different per country, since we use a different payment method in each country. E.g. in NL we’d use iDEAL, etc.
In what countries can you offer this? Do you have an alternative for the UK, France, Italy Spain, etc?
The major SEPA Direct Debit countries are Germany, Australia, The Netherlands and Belgium, in which we can offer this flow in combination with Sofort, GiroPay, EPS, iDEAL and Bancontact. UK is a different story altogether, because it is not a EUR country. We offer BACS Direct Debit as an alternative in GBP, but in general see much more traction with cards in the UK. France, Italy and Spain are EUR countries and can thus accept SEPA Direct Debit, but we see cards being more popular in these countries.
How do they consent to the recurring? Could you provide an example of the flow (screenshots)?
We leave this up to you on what you wish to communicate with the merchant. See below Spotify’s screen when selecting iDEAL (this is translated by Google Translate from Dutch to English). This is purely an example how can communicate towards your shoppers.
We advise to be clear in your communication to shoppers: shoppers can chargeback SEPA Direct Debits and they will more likely do this if they did not clearly get that you collect the bank account and use this for SEPA Direct Debits. Also a good option would e.g. to communicate per email to be transparent when you’re charging their bank account using SEPA Direct Debit.

On the legal front: shoppers are protected by the SEPA Direct Debit scheme, with the possibility to chargeback. This can be done very easily within the first 8 weeks, by clicking a single “refund”-button in their online banking app or website. From 8 weeks until 13 months the shoppers can theoretically request their bank (by contacting them) to chargeback a SEPA Direct Debit, in case the shopper deems the transaction as unauthorised. Would this happen, we can’t defend the chargeback since we don’t have a "formal consent” in the form of a signed mandate. In our data, we see 99.9% of all chargebacks happening within the first 8 weeks, which is why this type of “formal consent” would not weigh out the effort of collecting and storing paper signed mandates (and manually contacting the bank for defending such a claim).
The reason why we do believe it is important to communicate clearly is mostly to prevent chargebacks, but also to reduce any complaints and reputational damages.

In this case, what is the option for mandate?

2.) What we also offer is what Sophia mentioned before: when redirecting to our HPP we offer the shopper to set his (physical) signature on our HPP (by using touch screen or mouse). We do not share this with the shopper’s bank (since it doesn’t change the fact that the Direct Debit can easily be chargebacked), but it does make sure that shoppers are more consciously giving their consent to you/us for doing the Direct Debits from their bank account, which will less likely cause them to chargeback. It does not prevent a fraudster entering somebody else’s IBAN and put a cross in the signature box, since the signature isn’t actually checked against anything.

We see option 1 being used most often, since there is an actual account verification, and the flow is relatively smooth (or at least familiar, so good conversion). It works in the bigger SEPA Direct Debit countries (DE, AT, NL, BE), but not in all over Europe. However this flow does require you yourself as a merchant to clearly inform your shoppers that you will use the collected IBAN for any subsequent purchases using Direct Debit, to prevent complaints -> chargebacks.

I believe this is your official SEPA Direct Debit product, correct?
Both flows are using SEPA Direct Debit. But the first flow only uses SEPA Direct Debit for the recurring charges (while the first transaction is done via another payment method, this is also touched upon shortly in the above link in the section “recurring"), the second flow is also processing the first transaction via SEPA Direct Debit.
The major difference being that you for the second flow, the IBAN needs to be collected by other means, either you can collect it yourselves and pass it along in the payment request; or you can use our hosted payment page so the shopper can enter his IBAN.
Does this use the same flows as the option #1, but with the added signature on HPP?
In option #1 we don’t show a screen where the shopper can enter the IBAN, in this option we do, see e.g. the below (note that you can style the Hosted Payment Page can be fully customised in terms of look and feel).

And another one with the optional “Signature” field:

As I understand, this option is not truly the mandate (because it doesn't get registered by a certified Registration Authority or sent to the bank). Is that correct?
There is no "Registration Authority” involved. We do send the mandate related info (mandate id, creditor id, etc) to the bank as part of the SEPA Direct Debit payments, since these are mandatory fields, but for regular SEPA Direct Debits the actual mandate (incl shopper signature) does not need to be stored by any bank. Note that this is different for the special B2B scheme, which cannot be chargebacked, but requires the debtor (=payer) to register the mandate at their bank before the first charge. This flow doesn’t really fit well in e-commerce (note that the regular scheme can also be used for businesses).
I've heard of advanced electronic signature in Europe, where customer receives an SMS with a unique code that they enter on the mandate signature page. Is there anything like this on the roadmap?
There are a few local initiatives. E.g. in the Netherlands there is a relative new initiative by the Dutch Payment Association (who also own iDEAL). We don’t have concrete plans to integrate with this, because it doesn’t really solve any problem (shopper can still chargeback within the first 8 weeks) and is more expensive than our current solution (iDEAL - option #1 above, which we’d expect to have a much better conversion). The only case where we think it might be interesting is for pure B2B merchants. But, unfortunately there is no pan-European initiative.
I believe there's no real mandate there's also no mandate management (e.g.inactivate or block mandates if the chargeback information indicates that future usage will only result in fines imposed by the Debtor Bank, etc). Please confirm.
Correct; there is no such mandate management. As mentioned before the Debtor bank doesn’t store the mandate themselves, so they cannot deactivate it neither. A shopper can always easily refund any charge and is already informed one-day before collection that the payment is going to happen by their bank. Some specific banks can offer services to block an account from being debited, but for consumer accounts we hardly ever see this, since (esp. in NL, DE, BE and AT) consumers let most their recurring bills (rent, mortgage, telecom, insurance, etc) run via direct debits.
Around chargeback fees: yes, the debtor bank can charge these to us. We see especially higher additional fees from Germany and Austria (due to legacy regulations), but we don’t pass them on to you. Instead this is all blended in our standard chargeback fee.