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There have been many contributions on this topic, including the Testing Manifesto (by Karen Greaves and Samantha Laing) and  and the Agile Testing Quadrants (by Brian Marick & Lisa Crispin).

While the Testing Manifesto shows us how to look at testing in an Agile context and the mindset changes from "old ways" of looking at testing, the Agile Testing Quadrants provide a different perspective: what kinds of testing and tests there are, how can they be grouped, their purpose/fit and how to choose which testing to perform at any moment based on the quadrants and the risks we want to mitigate.

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Thus, by having coverage information always present, on the issues being worked out and also on the Agile Boards where team members manage and track their progress, everyone can see their real status (e.g. OK, NOK), which also makes everyone responsible for taking actions in order to make sure they are OK (i.e. properly tested).

Agile Testing Quadrants

The Agile Testing Quadrants (by Brian Marick & Lisa Crispin) provide a way to group different kinds of testing in 4 quadrants, considering whether they are business or technology facing and whether they are mostly used to support the team and guide development or to critique the product instead.

Quadrants are numbered although their number is just a mere reference to be used between team members.

The idea is to continuously assess risks and to mitigate them focusing on the quadrant(s) that can better target those risks.

Quoting Lisa Crispin: "Consider where the highest risk might be and where testing can add the most value.".

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What is clear from this diagram is that Tests can either be manual, automated or you even use some tools to help you perform certain types of tests (e.g. for load testing).

The value provided by each testing approach ("manual", exploratory, automated) and for each different type of tests is different and complements each other.

Xray may be used to manage all sorts of Tests and have visibility of their results and see how they impact on the related stories/epics.

In order to perform testing from the fourth quadrant (i.e. Q4) you may use whatever tools you want; likewise, for implementing automated tests you may use whatever automation framework covers best your needs, including Gherkin based ones (e.g. Cucumber, Behave, SpecFlow) among others. Xray does not enforce or add restrictions in using a specific tool whatsoever, thus your team can choose what they think is best and still track your testing progress in Xray.