Fully homomorphic encryption (FHE) would drastically improve the security of sensitive computations and in general of using Cloud and third party resources, by allowing to perform computations directly on encrypted data without the need to know the decryption key.
But as of today, fully homomorphic encryption is extremely inefficient making it impractical for general use. Still development is continuing and new results are achieved. For example recently IBM announced an Homomorphic Encryption Service, which is probably more like an online demo but the purpose seems to be to simplify the path for an early adoption by specially interested parties. But IBM is not alone and, among others, Google and Microsoft are developing Open Source libraries which can be used by a developer expert in cryptography to build for example end-to-end encrypted computation services where the users never need to share their keys with the service.