If you are 'partway through' something you have begun something but are still in the process of finishing it. If you are 'halfway through' something you are at the mid-point towards completion. You might use these expressions to give a status update or to say how close you are to finishing something. Similar to 'at the halfway point'.

1. I got quite bored watching the film in the cinema yesterday, so I ended up leaving halfway through.
2. I got halfway through 'A brief history of time' and then gave up reading it.
3. I am only partway through that series so I don't want any spoilers.

1. We are only partway through our recruitment process, so there are still many candidates left to interview.
2. There isn't much time left and we're not even halfway through the issues that needed discussing. Perhaps we should park it until our next meeting.
3. Partway through the build, we encountered some difficulties that slowed us down a little.