Via de Amore

Still closed and under construction. They're hoping it can reopen late next year.

Despite the intriguing name, that was not the part of the walk with the best view. I believe it was the easiest section, though, so best for those with mobility issues.

The Via dell' Amore was closed on 24 Sept. 2012 after a rock slide which injured four Australian tourists. It is still closed and will probably not be re-opening until at least 2019 (but that can change and it could be pushed back further). Repairs will reportedly cost about €5 million, so extensive work has to be done.

The Via dell' Amore is the easiest of the four Sentiero Azzurro trails, as it's mostly level and paved. A small part is open at the Manarola end and there's a small Cafe / Bar there (open seasonally ~April 1 - Sept. 30) were you can get a meal or enjoy a "cool one" while you enjoy the views.

The trail segment from Manarola to Corniglia has also been closed for a number of years due to a slide which can be seen in this photo. The trail runs along the same route as the light coloured poles.

The Corniglia - Vernazza and Vernazza - Monterosso segments have been open for the most part, but that can change at any time due to storm damage or whatever.

Great answer from Ken.
As he said, Via dell' Amore (592-1 (SVA2) Riomaggiore - Manarola) is not expected to open this coming 2018 season, and other trails in the CT can close at any time to damage or heavy weather. To check the current status of any trail, reference the park's website:

http://www.parconazionale5terre.it/Eindex.php
http://www.parconazionale5terre.it/Esentieri-outdoor.php

I passed the Via dell'Amore taking the ferry boat from Riomaggiore to Manarola in May (having "hiked" it in 2011 - it's really more of a stroll than a "hike"). I can see the slide in some zoomed in pictures I shot. There's no sign of any reconstruction work at all that I could see.

There's no sign of any reconstruction work at all that I could see.

I can't answer for what was going on last May but there have been reported funding issues affecting the trail's repair:

https://community.ricksteves.com/travel-forum/italy/cinque-terre-trail-closure

Anyway, the trail is currently closed, has been closed for some years now, and is not expected to re-open until 2019, last I read.

"There's no sign of any reconstruction work at all that I could see."

You can get some ideas of the type of reconstruction work if you walk up to the small bar at the Manarola end. Crews have been installing thick galvanized steel mesh, attached with rock anchors. That will hopefully contain any loose rock and keep it from falling onto the trail. I imagine that similar remediation work will be required on other parts of the trail, which will be expensive and time consuming. You can get some idea of the repair method from THIS photo.