We have started modernizing the search results page a few years ago. It is available on every site under this URL: /_layouts/15/search.aspx/siteall?q=myquery. Also the new search box placed in the suite header has started rolling out to modern experiences, and will be available broadly by end of June. We will be making it available to classic sites later this year as well. Some customers redirect their classic search boxes to the modern results page already.
The modern search experience is a part of the overall Microsoft Search experiences. See more details in this post: https://techcommunity.microsoft.com/t5/Microsoft-Search-Blog/Welcome-to-Microsoft-Search-intelligent-search-for-the-modern/ba-p/531156. We will be bringing additional improvements to it later in 2019, and early 2020 as well including custom refiners, verticals, result types with modern display templates, as well as custom pages that can use modern web parts.