I spend a fair amount of time working as an executive secretary for a volunteer organization. This is not something I aspired to do. Instead someone asked me to do it and I said I would. As an executive secretary I basically set appointments for people to meet with the leadership of the organization. Sometimes people ask to meet with the leaders and other times leaders ask to meet with specific people. Google's calendar, which can be found at https://calendar.google.com, does an amazing job and makes things very easy.
Before networked computers became commonplace, someone in my position had to keep paper calendars and have a lot of coordination meetings to make sure not to double-schedule someone. Now it is as simple as providing a scheduler like me with access to your calendar. Most of the leaders of the volunteer organization I associate with have e-mail addresses separate from their regular work or personal e-mail. Then they just log into Google Calendar with it and make sure to give me access to their calendar so I can set appointments for them.
The organization leadership changed significantly last week as nobody is expected to be a volunteer forever. We met as a new group on Wednesday evening and I deleted my access to the old leadership's calendars. The new leadership then shared their newly created e-mail addresses and gave me proper access. The next evening I then went through and created calendar entries for all of the regular meetings. We also had a number of requests for people to meet with the new leadership and I entered those. Fortunately I had lots of experience using Google Calendar in the past and did not have much of a learning curve.
I keep my personal calendar on my iPhone. I can access it from my Mac computer. It is great as I keep all sorts of appointment information up-to-date using both devices without having to worry about which one has the most correct information. They both do as an update on one pushes the change to the other. This would also be a great solution for the volunteer association I work with. The only downside is that everyone is required to use Apple products. Google Calendar doesn't care what phone you use. While you can access it with your phone's browser, there is also an application you can put on your phone. I just always use a web interface and it works great.
Are there problems with Google Calendar? Of course but they are minor. It has all of the features I need it for and appreciate the free price tag. If you are looking for a calendaring tool that makes it easy to share people's schedules, you might want to give it a look. It may also work for you.