Fully Homomorphic Encryption (FHE), which enables evaluation of arbitrary (non-encrypted) functions on encrypted data, and cryptographic program obfuscation (CPO), which enables evaluation of obfuscated programs/circuits for non-encrypted inputs, are two related hot topics of cryptography that have recently seen remarkable progress. FHE and CPO have a lot of potential high-impact applications in cloud computing, information sharing, machine learning, and a large number of other areas. Many recent advances in both FHE and CPO have come from the cryptographic primitives based on lattices. This talk reviews some of these advances and current capabilities/applications of lattice-based FHE and CPO protocols from the perspective of PALISADE, an open-source lattice cryptography library that is being developed by the NJIT Cybersecurity Research Center in collaboration with our partners in government, industry, and academia. The current challenges limiting the practicability of FHE and CPO are also discussed.