How to get current category in magento2?

Magento sets registry for categories being accessed. So, to get currenct category, use following method:

/**
 * @param \Magento\Framework\Registry $registry
 */

protected $_registry;

public function __construct(
    \Magento\Framework\Registry $registry
) {
    $this->_registry = $registry;
}

and then use:

$category = $this->_registry->registry('current_category');//get current category

Now you can access the collection and fetch details such as $category->getName()

The above to seem correct, but I think that jumping straight to the Registry is not the best approach. Magento provides a Layer Resolver that already encapsulates that functionality. (See the TopMenu Block in the Catalog Plugins)

I suggest injecting the \Magento\Catalog\Model\Layer\Resolver class and using that to get the current category. Here is the code :

<?php

namespace FooBar\Demo\Block;

class Demo extends \Magento\Framework\View\Element\Template
{
    private $layerResolver;

    public function __construct(
        \Magento\Framework\View\Element\Template\Context $context,
        \Magento\Catalog\Model\Layer\Resolver $layerResolver,
        array $data = []
    ) {
        parent::__construct($context, $data);

        $this->layerResolver = $layerResolver;
    }

    public function getCurrentCategory()
    {
        return $this->layerResolver->get()->getCurrentCategory();
    }
}

Here is what the actual getCurrentCategory() method does in the Resolver Class.

public function getCurrentCategory()
{
    $category = $this->getData('current_category');
    if ($category === null) {
        $category = $this->registry->registry('current_category');
        if ($category) {
            $this->setData('current_category', $category);
        } else {
            $category = $this->categoryRepository->get($this->getCurrentStore()->getRootCategoryId());
            $this->setData('current_category', $category);
        }
    }

    return $category;
}

As you can see, it does still use the registry but it provides a fallback in case that fails.