Currently, a user can only search the site if the user knows the name of the site or part of the name.
When a new site is created a lot of times users doesn't remember the name. Also, the site is not listed in the frequent or suggested sites.
I think, it would be useful if a list is displayed which contains all the sites that user has access to across the farm (not limiting to a particular site collection).

It would be great to have a column type for lists or libraries that stores a search-query.
In column settings you would create a query with a reference to the list-item (something like "author:{Item.Author} AND ContentType:Tasks").
This way you could dynamically link content to a list item.

In WSS 3.0 (SharePoint 2007), when we searched a blog, it gave us the option to sort results by Relevance (the default) or by Modified Date. Now in SharePoint Online, when you search a blog, it gives you no sort options, but seems to list the search results in random order. This is a step backwards in my opinion. We need to be able to sort by Modified Date again.

*English follows Japanese

Delve にて組織内のユーザーを検索することを制御したい
Delve 画面の左上の [検索] ボックスにユーザーの名前もしくはメール アドレスを入力しますと、ユーザーが検索されるようになりますが、検索できないように設定できる機能を追加してほしい。
---------------------------------------------------
I want to control the searchable of users in the organization on Delve
If I enter the user's name or email address in the search box at the top left of the Delve page, the users will be searched.
Please add a feature that can set users not to be searchable.

Allow adding/removing a file type to the search index in SharePoint online

We are about to build a search-driven Intranet with Communication Sites. Today we found out that there is a limit to the items shown in a hcwp, but we need it to be able to show all results found. A user must be able to "scroll" oder "page" through all content found by a managed property filter used in the hcwp. A hard cap limit to the results shown will break a search driven intranet, when content found can´t be viewed by the user because of a "view limit".

When sharing content in SharePoint Online, the sharing interface allows a user to type the name of an Office 365 Group. SharePoint Online content that is shared in this manner will not appear in SharePoint Search results to the members of the Office 365 Group. This doesn't provide a consistent experience for users, as many users may not be aware what entries are Office 365 Groups, Azure Active Directory security groups, etc. We'd like to see content shared to the members of an Office 365 group in this manner appear in the search results for those users.

So we can show search refiners for filtering results based on library name.

For manual download the OOTB SharePoint reports from SP admin page- SharePoint Online admin portal> Search> Search Reports.
Multiple reports available OOTB, but no API/Powershell available for Search Analytics, by which we can export custom Search reports or we can schedule the download of OOTB reports Monthly.

Provide API/Powershell for managing/automating SharePoint Search reports.

Enable some mechanism that allows a consumer to provide feedback on the results they get in search (e.g. not getting expected results or feedback tied directly to a specific content item). General feedback would be routed to one place while content item level feedback would be automatically routed to the assigned author.

Wanted to display items when certain field is not empty.
If possible please share us why it's not implemented?

It would be very beneficial, to be able to use word extraction in SharePoint Online, i.e. be able to supply your own custom dictionary, used to extract certain words from search for use in e.g. refiners.

Integrate Delve Search results with SharePoint search center

Currently we have a large amount of file share and SharePoint data that contains Personally Identifiable Information and Sensitive Data. It would be ideal to be able to auto tag documents at the index level to filter out those documents in Search results. Additionally, it would also allow for tagging documents in a positive way, for more refined searching.

Make it easier to add/remove servers from the Search Service Application.

Using the search at the top left of the site contents page has a filtering impact on the contents and subsites listings. This functionality is a complete divergence from the search experience in other parts of SharePoint. There should be a way to send all search boxes to the same search results page, instead of this rather confusing setup.

I want to have "search" function in recycle bin.

Allow to add custom file extension type like .DWG etc. so that search results could be able to link to actual file like .pdf etc.